Piotr Pragacz Home Page

List of Publications

Book:

Schubert Varieties and Degeneracy Loci, Lecture Notes in Math. vol.1689,
Springer, Berlin 1998 (with W. Fulton)

Edited books:

E1. Parameter Spaces; enumerative geometry, algebra and combinatorics,
Banach Center Publications 36, Warsaw 1996

E2. Algebraic Geometry: Hirzebruch 70, Contemporary Mathematics AMS 241,
Providence R.I. 1999 (with M. Szurek and J. Wisniewski)

E3. Proceedings of the AGAAP Conference 2003, Serdica Mathematical Journal
30 (2-3), 2004 (with V. Brinzanescu and V. Drensky)

E4. Topics in cohomological studies of algebraic varieties; Impanga Lecture Notes,
Trends in Mathematics, Birkhauser 2005.

E5. Algebraic cycles, sheaves, shtukas, and moduli; Impanga Lecture Notes,
Trends in Mathematics, Birkhauser 2008

E6. Hoene-Wronski: Zycie, Matematyka i Filozofia, Publications of IM PAN,
Warszawa 2008 (in Polish)

E7. Contributions to Algebraic Geometry; Impanga Lecture Notes, EMS
Ser. Congr. Rep., EMS Publ. House, Zurich 2012

Research papers:

1. Syzygies des Pfaffiens, C. R. Acad. Sci. Paris, 287, Serie I (1978), 89-91

2. Ideals generated by Pfaffians, Journal of Algebra 61 (1979), 189-198
(1, 2 with T. Jozefiak)

3. On the syzygies of Grassmannians, Preprint of IM PAN Torun, 16 pp.,
1980 (with J. Weyman)
(published partially in 10)

4. Resolutions of determinantal varieties and tensor complexes associated with
symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109-189 (with
T. Jozefiak and J. Weyman)

5. Classes of determinantal varieties associated with symmetric and
antisymmetric matrices, Algebraic Geometry, Bucharest 1980, Teubner Texte zur
Mathematik 40 (1981), 106-108

6. Classes of determinantal varieties associated with symmetric and
skew-symmetric matrices, Izwiestja AN SSSR, vol. 45, no. 9 (1981), 662-673
(in Russian); English translation: vol. 18 (1982), 575-586
(announced in 5)
(5, 6 with T. Jozefiak and A. Lascoux)

7. Characteristic free resolution of (n-2)-order Pfaffians of nxn antisymmetric
matrix, Journal of Algebra 78 (1982), 386-396

8. Equerres et fonctions de Schur, C. R. Acad. Sci. Paris, 299, Serie I (1984), 955-958
(with A. Lascoux)

9. Complexes associated with trace and evaluation; another approach to
Lascoux's resolution, Advances in Mathematics 57 (1985), 163-207
(published version of the IRMA Strasbourg Preprint no.208/P-120, 1983)

10. On the construction of resolutions of determinantal ideals: a survey,
Seminaire d'Algebre Dubreil-Malliavin 1985 (M.-P. Malliavin ed.) Springer Lect. Notes
in Math. 1220 (1986), 73-92
(9, 10 with J. Weyman)

11. A new proof of the Giambelli-Thom-Porteous formula, Preprint of IM PAN
Torun, 5 pp., 1985
(published in 37)

12. Foncteurs de Schubert, C. R. Acad. Sci. Paris, 304, Serie I (1987), 209-211
(with W. Kraskiewicz)

13. Determinantal varieties and symmetric polynomials, Functorial Analysis and
Its Applications, 21 (1987), 89-90 (in Russian); English translation: (1988), 249-251

14. A note on the elimination theory, Indagationes Math. 49 (1987), 215-221
(announced partially in 13; an extended version of the IMPAN preprint
"A note on the elimination theory I, 1986)

15. Ribbon Schur functions, European Journal of Combinatorics 9 (1988), 581-592

16. S-function series, Journal of Physics A: Math. Gen. 21 (1988), 4105-4114
(15, 16 with A. Lascoux)

17. Enumerative geometry of degeneracy loci, Ann. scient. Ec. Norm. Sup.
4e Serie, 21 (1988), 413-454
(partially announced in 13; an extended version of the IMPAN preprints
"Degeneracy loci and symmetric functions I and II, 1986)

18. On the generic free resolutions, Journal of Algebra 128 (1990), 1-44
(with J. Weyman)

19. Cycles of isotropic subspaces and formulas for symmetric degeneracy loci,
Topics in Algebra, Banach Center Publications, Polish Scientific Publishers (S. Balcerzyk
et al. eds.) vol. 26 (2) (1990), 189-199

20. Euler characteristic of degeneracy loci, Preprint of MPI Bonn no.68, 1990 (with
A. Parusinski)
(published in 33)

21. Algebro-geometric applications of Schur S- and Q-polynomials, in
"Topics in Invariant Theory", Seminaire d'Algebre Dubreil-Malliavin 1989-1990
(M-P. Malliavin ed.), Springer Lect. Notes in Math. 1478 (1991), 130-191
(published version of the Dept. Math. KTH Stockholm Preprint no.14, 1988;
contains the IMPAN preprint "A note on the elimination theory II", 1986)

22. A determinantal formula for skew Q-functions, Journal of the London
Mathematical Society, (2) 43 (1991), 76-90 (with T. Jozefiak)

23. Characteristic numbers of degeneracy loci, in Enumerative Algebraic Geometry,
Proceedings of "The 1989 Zeuthen Symposium", Contemporary Mathematics
AMS 123 (1991), 189-197 (with A. Parusinski)
(published version of the Dept. Math. Univ. Ferrara Prepint no.147, 1990)

24. Cohomology of Schubert subvarieties of Gl_n/P, Journal of Differential
Geometry 35 (1992), 511-519 (with E. Akyildiz and A. Lascoux)
(published version of the Dept. Math. King Fahd Univ. Petroleum and Minerals
Preprint no.112, 1989)

25. On a Jacobi-Trudi formula for supersymmetric polynomials,
Advances in Mathematics, 95 (1992), 8-17 (with A. Thorup)
(published version of the Dept. Math. Copenhagen Univ. Preprint no.16, 1990)

26. Pieri type formula for isotropic Grassmannians; the operator approach,
Manuscripta Math. 79 (1993), 127-151 (with J. Ratajski)
(published version of the MPI Bonn Preprint No.9, 1992)

27. Geometric applications of symmetric polynomials; some recent developments,
MPI Bonn Preprint No.16 (1992)
(published in 37)

28. A Pieri-type formula for Sp(2m)/P and SO(2m+1)/P, C. R. Acad. Sci. Paris, 317,
Serie I (1993), 1035-1040
(published version of the IHES Preprint no.4 , 1993)

29. Formulas for some symplectic and orthogonal degeneracy loci,
manuscript 11 pp., Math. Inst. Polish Acad. Sci., Torun, August 1993
(published in 38)
(28, 29 with J. Ratajski)

30. Divided differences and ideals generated by symmetric polynomials,
Discrete Mathematics, 126 (1994), 209-215 (with A. Lascoux)
(published version of the Dept. Math. Univ. Bergen Preprint no.59-25-04-91)

31. Polynomials homologically supported on degeneracy loci, Ann. della Scuola
Normale Superiore di Pisa, Serie IV, 23(1) (1996), 99-118 (with J. Ratajski)
(published version of the Dept. Math. Univ. Bergen Preprint no.61-25-10-91)

32. A formula for the Euler characteristic of singular hypersurfaces, Journal
of Algebraic Geometry, 4 (1995), 337-351
(published version of the Dept. Math. Univ. Sydney Preprint no.16, 1994)

33. Chern-Schwartz-MacPherson classes and the Euler characteristic of
degeneracy loci and special divisors, Journal of the Amer. Math. Soc. 8
(1995), 793-817
(published version of the Dept. Math. Univ. Sydney Preprint no.17, 1994 )
(32, 33 with A. Parusinski)

34. Fundamental classes, diagonals and Gysin maps, Preprint of MPI Bonn
no.141, 1995
(published in 37 and 38)

35. A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians,
J. reine angew. Math. 476 (1996), 143-189 (with J. Ratajski)
(published version of the MPI Bonn Preprint no.15, 1994)

36. On the class of Brill-Noether loci for Prym varieties, Math. Annalen 302
(1995), 687-697 (with C. De Concini)
(extended and published version of the SNS Pisa Preprint no.17, 1994)

37. Symmetric polynomials and divided differences in formulas of intersection
theory, in "Parameter Spaces", Banach Center Publications, vol. 36 (1996), 125-177
(extended and published version of 27 and arXiv:alg-geom/9605014)

38. Formulas for Lagrangian and orthogonal degeneracy loci; \~Q-polynomial
approach, Compositio Math. 107 (1997), 11-87 (with J. Ratajski)
(extended and published version of the MPI Bonn Preprint no.132, 1994
and arXiv:alg-geom/9602019)

39. A generalization of the Macdonald-You formula, Journal of Algebra 204 (1998),
573-587 (published version of the IM PAN Warsaw Preprint no.573, 1997)

40. Operator calculus for \~Q-polynomials and Schubert polynomials, Advances in
Mathematics 140 (1998), 1-43

41. Schur Q-functions and degeneracy locus formulas for morphisms with
symmetries, in "Recent Progress in Intersection Theory", G. Ellingsrud,
W. Fulton, and A. Vistoli eds., Trends in Mathematics, Birkhauser, 2000, 239-263
(published version of arXiv/9901126)
(40, 41 with A. Lascoux)

42. Addendum to : ''A generalization of the Macdonald-You formula'', Journal
of Algebra 226 (2000), 639-648
(published version of the note "Restricting Schubert classes": arXiv math/9907092)

43. Orthogonal divided differences and Schubert polynomials, \~P-polynomials,
and vertex operators, in the special volume 48 of Michigan Mathematical Journal,
in honor of William Fulton (2000), 417-441 (with A. Lascoux)
(published version of arXiv:math/0008006)

44. The degrees of Schubert varieties on SO(2n+1)/U(n), Preprint of Inst.Math.Chinese
Acad. Sci. Beijing, 9 pp., 2001 (with D. Haibao)
(published in 48)

45. Characteristic classes of hypersurfaces and characteristic cycles, Journal of
Algebraic Geometry 10 (2001), 63-79 (with A. Parusinski)
(published version of the Dept. Math. Univ. Angers Preprint no.51, 1998
and arXiv:math/9801102)

46. Jacobians of symmetric polynomials, Annals of Combinatorics 6 (2002), 169-172

47. Double Sylvester sums for subresultants and multi-Schur functions, Journal of
Symbolic Computation 35(6) (2003), 689-710
(published version of the MPI Bonn Preprint no.30, 2001)
(46, 47 with A. Lascoux)

48. Divided differences of type D and the Grassmannian of complex structures, in:
''Algebraic Combinatorics and Quantum Groups'', N. Jing ed., World Scientific (2003),
31-60 (with H. Duan)
(published version of the MPI Bonn Preprint no.107, 2001)

49. A Pieri-type formula for even orthogonal Grassmannians, Fundamenta
Mathematicae 178 (2003), 49-96 (with J. Ratajski)
(published version of the MPI Bonn Preprint no.83, 1996)

50. Architectonique des formules preferees d'Alain Lascoux in: "LascouxFestSchrift",
Seminaire Lotharingien de Combinatoire 52 (2005), Article B52d, 39 pp.

51. Schubert functors and Schubert polynomials, in the special volume of European
Journal of Combinatorics 25/8 in honour of Alain Lascoux (2004), 1327-1344
(with W. Kraskiewicz)
(announced in 12; extended and published version of the authors' Dept. Math.
Univ. Torun Preprint, 1986 )

52. Multiplying Schubert classes, in "Topics in cohomological studies of algebraic
varieties", Trends in Mathematics, Birkhauser (2005) 163-174

53. Bezoutians, Euclidean algorithm, and orthogonal polynomials, Annals of
Combinatorics 9 (2005), 301-319 (with A. Lascoux)

54. Formulas for \~Q-functions: a survey for Brian in: "Symmetry, Spectroscopy,
and SCHUR", Proceedings of the Brian Wybourne Commemorative Meeting
(R.C. King et al. eds.), N. Copernicus Press, Torun (2006), 231-240

55. Thom polynomials and Schur functions I, math.AG/0509234
(published in 57, 59 and 64)

56. Positivity of Schur function expansions of Thom polynomials, Fundamenta
Mathematicae 195 (2007), 85-95 (with A. Weber)
(extended and published version of the MPI Bonn Preprint no.60, 2006
and arXiv:math/0605308)

57. Thom polynomials and Schur functions: the singularities I_{2,2}(-), Annales
de l' Institut Fourier 57 no. 5 (2007), 1487-1508
(extended and published version of the MPI Bonn Preprint no.83, 2006
and arXiv:0705.1375)

58. Diagonal subschemes and vector bundles, Pure and Applied Mathematics
Quaterly vol.4, no.4, part 1 of 2, Special Issue in honor of Jean-Pierre Serre
(2008), 1233-1278 (with V. Pati and V. Srinivas)
(published version of the MPI Bonn Preprint no.110, 2006 and
arXiv:math/0609381)

59. Thom polynomials and Schur functions: towards the singularities A_i(-) ,
in: "Real and complex singularities - Sao Carlos 2006", Contemporary Mathematics
AMS 459, (2008) 165-178
(extended and published version of the MPI Bonn Preprint no.139, 2006
and arXiv:0810.2441)

60. Miscellany on the zero schemes of sections of vector bundles, (notes by
O. Ozturk), in "Algebraic cycles, sheaves, shtukas, and moduli", Trends in
Mathematics, Birkhauser, 2008, 105-116

          61. Thom polynomials of invariant cones, Schur functions, and positivity, in:
           "Algebraic cycles, sheaves, shtukas, and moduli, Trends in Mathematics, Birkhauser,
           2008, 117-129 (with A. Weber)
           (published version of arXiv:0709.1191)

          62. Positivity of Thom polynomials II: the Lagrange singularities, Fundamenta
          Mathematicae 202 (2009), 65-79 (with M. Mikosz and A. Weber)
          (published version of arXiv:0710.5251)

               63. A note on the Chow groups of projective determinantal varieties ,
               an appendix to [G. and M. Kapustka "A cascade of determinantal Calabi-Yau
               threefolds"], Math. Nachrichten 283(12) (2010), 1829–1832

          64. Thom polynomials and Schur functions: the singularities A_3(-),
          Publ. RIMS Kyoto Univ. 46 (2010), 183-200 (with A. Lascoux)
          (published version of the RIMS Kyoto Preprint no.1638, 2008
          and arXiv:0810.2445)

          65. Positivity of Legendrian Thom polynomials, Journal of Differential
          Geometry 89(1) (2011), 111-132 (with M. Mikosz and A. Weber)
          (published version of arXiv:1005.1283)

          66. On Schur function expansions of Thom polynomials in "Contributions to
          Algebraic Geometry", EMS Ser.Congr.Rep., EMS Publ. House, Zurich 2012,
          443-479 (with O. Ozturk)
          (published version of arXiv:1111.6612)

          67. Positivity of Thom polynomials and Schubert calculus, Advanced Studies
          in Pure Mathematics Vol. 71 (2016) "Schubert Calculus - Osaka 2012" pp. 419-451
          (published version of arXiv:1304.2573)

        68. A Gysin formula for Hall-Littlewood polynomials, Proc. Amer. Math. Soc. 143
         (2015) no.11, 4705-4711; Corrigenda 144 (2016) no.7 p. 3197
          (arXiv:1403.0788)

69. Diagonals of flag bundles (with S. Kaji)
(arXiv: 1503.03217)

          70. Universal Gysin formulas for flag bundles, International Journal
          of Mathematics Vol. 28, No.11 (2017) 1750077 (23 pages) (with L. Darondeau)
          (arXiv: 1510.07852)

          71. On a certain family of U(b)-modules, in: "Schubert varieties, equivariant
          cohomology and characteristic classes, IMPANGA 15", EMS Ser. Congr. Rep.,
EMS Publ. House, Zurich (2018), 203-224
           (arXiv: 1603.0018)

          72. Gysin maps, duality, and Schubert classes, Fundamenta Mathematicae
   244 (2019), 191-208 (with L. Darondeau)
          (arXiv: 1602.01983)

          73. Flag bundles, Segre polynomials, and push-forwards, in "Schubert
          Calculus and its applications in combinatorics and representation theory",
          Springer Proceedings in Mathematics & Statistics 332 (2020), 17-25
         (with L. Darondeau)
        (arXiv: 1802.09039)

          74. Order of tangency between manifolds, in "Schubert Calculus and its
          applications in combinatorics and representation theory", Springer Proceedings
          in Mathematics & Statistics 332 (2020), 27-42 (with W. Domitrz and P. Mormul)
          (arXiv: 1803.07664)

          75. On some properties of the Łojasiewicz exponent, Comptes Rendus.
           Mathematique, Volume 359 (2021), no.8 p. 991-997
           (with Ch. Eyral and T. Mostowski)
          (arXiv:2003.13031)

Other publications:

            O1. Status XV problemu Hilberta w roku 1993, in "Problemy Hilberta", Publications
            of Institute of History of Sciences of Polish Academy of Sciences, Warszawa 1997,
            175-184 (in Polish)

            O2. Geometria enumeratywna rozmaitosci osobliwych, in "Dzialalnosc naukowa:
            wybrane zagadnienia", Polska Akademia Nauk, Warszawa 2000, no.9, 111-113
            (in Polish)

O3. Zycie i dzielo Alexandra Grothendiecka, Wiadomosci Matematyczne 40 (2004)
107-127 (in Polish)

O4. Zycie i dzielo Jozefa Marii Hoene-Wronskiego, Wiadomosci Matematyczne
43 (2007) 67-86 (in Polish)

O5. Jaroslaw Wlodarczyk pierwszym laureatem Nagrody IM PAN, Wiadomosci
Matematyczne 46(1) (2010) 95-96 (in Polish),

O6. Dziesiec lat Impangi, Wiadomosci Matematyczne 47(1) (2011) 45-54 (in Polish)

O7. A memorial writing: Alain Lascoux (1944-2013), 2 pp., Advanced Studies
in Pure Mathematics Vol. 71 (2016) "Schubert Calculus - Osaka 2012"

O8. IMPANGA 2000-2015, in NEWSLETTER of IMPAN, Spring 2015, 8-9

O9. Friedrich Hirzebruch - garść reminiscencji, Wiadomosci Matematyczne
52(1) (2016) 37-51 (in Polish)

O10. Biogram Piotra Michała Pragacza, Zlota Ksiega Nauki Polskiej
vol. II, p. 302 (2020) (in Polish)

Translations and reeditions:

          T1. Notes on the life and work of Alexander Grothendieck, (translated from [O3] by
             J. Adamus), in "Topics in cohomological studies of algebraic varieties", Trends in
             Mathematics, Birkhauser, 2005, xi-xxviii

T2. Life and work of Alexander Grothendieck, (translated from [O3] by
A. Shenitzer), American Mathematical Monthly 113(9), November 2006, 831-846

             T3. Notes on the life and work of Jozef Maria Hoene-Wronski, (translated from
             [O4] by J. Spalinski), in "Algebraic cycles, sheaves, shtukas, and moduli", Trends in
             Mathematics, Birkhauser, 2007, 1-20

T4. Jozef Maria Hoene-Wronski'nin Hayati ve Calismalari Uzerine Notlar,
(translated into Turkish from [T3] by O. Ozturk), "Oyun"- the Journal of "Turk Zeka
Vakfi" (Turkish Ingenuity Foundation), June 2008, 4-7 and 52-58

T5. Zycie i dzielo Jozefa Marii Hoene-Wronskiego in "Hoene-Wronski: Zycie,
Matematyka i Filozofia", IM PAN Publications 2008, 7-26 (in Polish; a modified
version of [O4])

          T6. La vita e l'opera di Jozef Maria Hoene-Wronski, (extension of [O4] for an Italian
   reader; translation from [O4], [T3] by M. Jarosz, L. Gatto and F. Mori), Atti della
             Accademia Peloritana - Classe di Scienze Fisiche, Matematiche e Naturali vol. 89
             no.1 (2011) 19 pp.

            T7. Friedrich Hirzebruch - a handful of reminiscences (extension of [O9]; translation
            from [O9] by Masha Vlasenko), in: "Schubert varieties, equivariant cohomology
            and characteristic classes, IMPANGA 15", EMS Ser. Congr. Rep., EMS Publ. House,
            Zurich (2018), 9-23

Notes from lectures:

N1. M. Atiyah: Physics and Geometry: a look at the last twenty years , in
"Algebraic Geometry: Hirzebruch 70", Contemporary Mathematics AMS 241 (1999)
1-8 (notes by P. Pragacz)

N2. J. Schuermann: Lectures on characteristic classes of constructible functions,
in "Topics in cohomological studies of algebraic varieties", Trends in Mathematics,
Birkhauser, 2005, 175-201 (notes by P. Pragacz and A. Weber)

Unpublished notes:

The LLPT Notes (with D. Laksov, A. Lascoux, and A. Thorup) edited by
A. Thorup (1995), available at http: //web.math.ku.dk/noter/filer/sympol.pdf

Also:

Humor w matematyce, "Konspekt", Krakow, 1/2007 (28), 106-116 (in Polish)

Corrections to [1]-[68]

Corrections to [69]-... and [Oi], [Ti]

(30.09.2021)

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