Flops and Hilbert schemes of space curve singularities

Abstract

Using pagoda flop transitions between smooth projective threefolds, a relation is derived between the Euler numbers of moduli spaces of stable pairs which are scheme-theoretically supported on a fixed singular space curve and Euler numbers of Flag Hilbert schemes associated to a plane curve singularity. When the space curve singularity is locally complete intersection, one obtains a relation between the latter and Euler numbers of Hilbert schemes of the space curve singularity. It is also shown that this relation yields explicit results for a class of torus-invariant locally complete intersection singularities.

v3: 79 pages, Final version, to appear in Journal of Algebraic Geometry. v2: 67 pages, some technical assumptions removed, typos fixed, main results unchanged. v1: 52 pages

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