Severi Degrees in Cogenus 4

Abstract

In this paper, we give closed-form formulae for Severi degrees in cogenus 3 and 4 using Ran's method. These formulae coincide with those of I. Vainsencher and for cogenus 3 case, that of J. Harris and R. Pandharipande. Another result of this paper is that we calculate the degree of the polynomial $N(\pi ,\delta ,d)$ in $d$, which is the degree of the locus of curves $C$ in P^2 with degree d having $\delta$ nodes and $C\cap L$ is of type $\pi$ to fixed line L. Using this result, we also calculate the coefficients of two leading terms of Severi polynomial, $N(\delta ,d)$.

TeX-Type: AMSLaTeX v 1.1, 11 pages

References in corpus (2)

• Enumeration of $n$-fold tangent hyperplanes to a surface
• On the quantum cohomology of the plane, old and new

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