Intersection of analytic curves
Volume 80 / 2003
Annales Polonici Mathematici 80 (2003), 193-202
MSC: 14C17, 32B15.
DOI: 10.4064/ap80-0-16
Abstract
We give a relation between two theories of improper intersections, of Tworzewski and of Stückrad–Vogel, for the case of algebraic curves. Given two arbitrary quasiprojective curves $V_{1},V_{2}$, the intersection cycle $V_{1}\bullet V_{2}$ in the sense of Tworzewski turns out to be the rational part of the Vogel cycle $v(V_{1},V_{2})$. We also give short proofs of two known effective formulae for the intersection cycle $V_{1}\bullet V_{2}$ in terms of local parametrizations of the curves.
