Enumeration of $n$-fold tangent hyperplanes to a surface

Details Enumeration of $n$-fold tangent hyperplanes to a surface Enumeration of $n$-fold tangent hyperplanes to a surface

1993-12-21

arxiv.org/abs/alg-geom/9312012v2

Mathematics

Algebraic Geometry

34 pages, Latex (Corrects Latex errors of previous version, minor changes)

Scientific paper

For each $1\leq n\leq6$ 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 \p{n} 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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