Karol Palka's homepage

Research interests and publications

Main research interests: algebraic geometry and topology, low-dimensional

varieties and log varieties - their structure, singularities, automorphisms,

group actions and embeddings; birational geometry, minimal model

program, quantum field theory and string theory.

Publications:

15. Completions of affine spaces into Mori fiber spaces with non-rational

fibers (with A. Dubouloz and T. Kishimoto),

J. Lond. Math. Soc. 106 (2022), No. 2, 1257-1290.

[140 pkt., IF=1,137], arXiv:2010.05884

14. Complex planar curves homeomorphic to a line have at most four

singular points, (with M. Koras)

J. Math. Pures Appl. 158 (2022), 144-182,

[200 pkt., IF=2,464], arXiv:1905.11376

13. Classification of planar rational cuspidal curves. II. Log del Pezzo

models (with T. Pełka),

Proc. Lond. Math. Soc. 120 (2019), No. 5, 642-703,

[140 pkt., IF=1,303], arXiv:1810.08180

12. Cuspidal curves, minimal models and Zaidenberg's finiteness

conjecture,

J. Reine Angew. Math. (Crelle's Journal) 747 (2019), 147-174

[200 pkt., IF=1,713], arXiv:1405.5346

11. The Jacobian Conjecture fails for pseudo-planes (with A. Dubouloz),

Adv. Math. 339 (2018), 248-284,

[200 pkt., IF=1,688], arXiv:1701.01425

10. The Coolidge-Nagata conjecture (with M. Koras),

Duke Math. J. 166 (2017), No. 16, 3085-3145,

[200 pkt., IF=2,403], arXiv:1502.07149

9. Classification of planar rational cuspidal curves. I. C**-fibrations (with

T. Pełka),

Proc. Lond. Math. Soc. 115 (2017), No. 3, 638-692,

[140 pkt., IF=1,303], arXiv:1609.03992

8. The geometry of sporadic C*-embeddings into C2 (with M. Koras and P.

Russell),

J. Algebra, 456 (2016), 207-249,

[100 pkt., IF=0,89], arXiv:1405.6872

7. A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-

Suzuki,

J. Algebra Appl. 14 (2015), No. 9, 1540012 (15 p.),

[70 pkt., IF=0,61], arXiv:1405.5391

6. The Coolidge-Nagata conjecture, part I,

Adv. Math. 267 (2014), 1-43,

[200 pkt., IF=1,688], arXiv:1405.5917

5. Classification of singular Q-homology planes I. Structure and

singularities,

Israel J. Math. 195 (2013), 37-69,

[100 pkt., IF=0,907], arXiv:0806.3110

4. Singular Q-homology planes of negative Kodaira dimension have

smooth locus of non-general type (with M. Koras),

Osaka J. Math. 50 (2013), 61-114;

[70 pkt., IF=0,375], arXiv:1001.2256

3. Classification of singular Q-homology planes II. C^1- and C*-rulings,

Pacific J. Math. 282-2 (2012), 421-457,

[100 pkt., IF=0,817], arXiv:1201.2463

2. Exceptional singular Q-homology planes,

Ann. Inst. Fourier, 61 (2011), no. 2, 745-774,

[140 pkt., IF=0,968], arXiv:0909.0772

1. Recent progress in the geometry of Q-acyclic surfaces,

CRM Proceedings and Lecture Notes, 54 (2011), 271-287, arXiv:1003.2395