Bulletin of the Belgian Mathematical Society - Simon Stevin

The characteristic numbers of cuspidal plane cubics in $\mathbb P^3$

Xavier Hernández and Josep M. Miret

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Abstract

We obtain the characteristic numbers of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$, namely, the non-zero intersection numbers which arise from considering 10 (possibly repeated) conditions from among the following: $P$, that the cuspidal cubic go through a point; $\nu$, that the cuspidal cubic intersect a line; and $\rho$, that the cuspidal cubic be tangent to a plane. In order to reach this goal, we consider a suitable compactification of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$ and we calculate, using several degeneration formulae, some of its non-zero intersection numbers, including all the characteristic ones.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 1 (2003), 115-124.

Dates
First available in Project Euclid: 10 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1047309418

Digital Object Identifier
doi:10.36045/bbms/1047309418

Mathematical Reviews number (MathSciNet)
MR2032330

Zentralblatt MATH identifier
1033.14020

Subjects
Primary: 14N10: Enumerative problems (combinatorial problems) 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]

Keywords
cuspidal cubics characteristic numbers

Citation

Hernández, Xavier; Miret, Josep M. The characteristic numbers of cuspidal plane cubics in $\mathbb P^3$. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 1, 115--124. doi:10.36045/bbms/1047309418. https://projecteuclid.org/euclid.bbms/1047309418


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