Virtual invariants of Quot schemes of points on threefolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913898683170816 |
|---|---|
| author | Mizyuk, Solomiya |
| author_facet | Mizyuk, Solomiya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual invariants of Quot schemes of points on threefolds Mizyuk, Solomiya Algebraic Geometry 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. |
| title | Virtual invariants of Quot schemes of points on threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.14490 |