Sheaves on surfaces and virtual invariants
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908306161795072 |
|---|---|
| author | Göttsche, L. Kool, M. |
| author_facet | Göttsche, L. Kool, M. |
| contents | Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection numbers, such as virtual Euler characteristics, Verlinde numbers, and Segre numbers. We survey a set of recent conjectures by the authors for these numbers with applications to Vafa-Witten theory, $K$-theoretic S-duality, a rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula, and a virtual Segre-Verlinde correspondence. A key role is played by Mochizuki's formula for descendent Donaldson invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_12730 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sheaves on surfaces and virtual invariants Göttsche, L. Kool, M. Algebraic Geometry High Energy Physics - Theory Differential Geometry 14D20, 14D21, 14J60, 14J80, 14J81 Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection numbers, such as virtual Euler characteristics, Verlinde numbers, and Segre numbers. We survey a set of recent conjectures by the authors for these numbers with applications to Vafa-Witten theory, $K$-theoretic S-duality, a rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula, and a virtual Segre-Verlinde correspondence. A key role is played by Mochizuki's formula for descendent Donaldson invariants. |
| title | Sheaves on surfaces and virtual invariants |
| topic | Algebraic Geometry High Energy Physics - Theory Differential Geometry 14D20, 14D21, 14J60, 14J80, 14J81 |
| url | https://arxiv.org/abs/2007.12730 |