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arXiv · 2506.14490

Virtual invariants of Quot schemes of points on threefolds

Solomiya Mizyuk
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Abstract

We construct an almost perfect obstruction theory of virtual dimension zero on the Quot scheme parametrizing zero-dimensional quotients of a locally free sheaf on a smooth projective $3$-fold. This gives a virtual class in degree zero and therefore allows one to define virtual invariants of the Quot scheme. We compute these invariants proving a conjecture by Ricolfi. The computation is done by reducing to the toric case via cobordism theory and a degeneration argument. The toric case is solved by reducing to the computation on the Quot scheme of points on $\mathbb{A}^3$ via torus localization, the torus-equivariant Siebert's formula for almost perfect obstruction theories and the torus-equivariant Jouanolou trick.

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Solomiya Mizyuk. 2025-06-17. Virtual invariants of Quot schemes of points on threefolds. https://arxiv.org/abs/2506.14490

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