Enumeration of n-fold tangent hyperplanes to a surface

1993/12/21 by Israel Vainsencher, Vainsencher, Israel · 9 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.alg-geom/9312012

openalex publication_date 1993/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each 1≤ n≤6 we present formulas for the number of n-nodal curves in an n-dimensional linear system on a smooth, projective surface. This yields in particular the numbers of rational curves in the system of hyperplane sections of a generic K3-surface imbedded in \pn by a complete system of curves of genus n as well as the number \bf17,601,000 of rational (\em singular) plane quintic curves in a generic quintic threefold.

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