English

Flops and Hilbert schemes of space curve singularities

Algebraic Geometry 2026-03-06 v3 High Energy Physics - Theory

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.

Keywords

Cite

@article{arxiv.2303.17154,
  title  = {Flops and Hilbert schemes of space curve singularities},
  author = {Duiliu-Emanuel Diaconescu and Mauro Porta and Francesco Sala and Arian Vosoughinia},
  journal= {arXiv preprint arXiv:2303.17154},
  year   = {2026}
}

Comments

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