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arXiv · 2303.17154

Flops and Hilbert schemes of space curve singularities

Duiliu-Emanuel Diaconescu·Mauro Porta·Francesco Sala·Arian Vosoughinia
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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.

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Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala, Arian Vosoughinia. 2023-03-30. Flops and Hilbert schemes of space curve singularities. https://doi.org/10.1090/jag/849

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