The punctual Hilbert schemes for the curve singularities of types E₆ and E₈

2011/09/23 by Sōma, Yoshiki, Watari, Masahiro · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.4991

Abstract

Pfister and Steenbrink studied punctual Hilbert schemes for irreducible curve singularities. In particular, they investigated the structure of special punctual Hilbert schemes for certain monomial curve singularities. In this paper, we study the punctual Hilbert schemes of all degrees for the curve singularities of types E₆ and E₈. For our analysis, we introduce computational algorithms to decompose a punctual Hilbert schemes into affine cells. We also use the theory of Gröbner basis and known results about the compactified Jacobian of singular curves to prove our main theorems.

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• On the geometry of punctual Hilbert schemes on singular curves and their motivic zeta functions
• Topology of the punctual Hilbert schemes of plane curve singularities with a single Puiseux pair

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