Intersection of analytic curves

Volume 80 / 2003

Tadeusz Krasiński, Krzysztof Jan Nowak 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.

Authors

  • Tadeusz KrasińskiFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland
    e-mail
  • Krzysztof Jan NowakInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
    e-mail

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