Rank-one sheaves and stable pairs on surfaces
| Autor: | Goller, Thomas, Lin, Yinbang |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2022.108322 |
| Popis: | We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a surface with irregularity 0, agrees with the usual deformation-obstruction theory. The perfect obstruction theory defines a virtual fundamental class on the moduli space. Using the embedding, we show that the virtual class equals the Euler class of a vector bundle on the smooth ambient space. As an application, we show that on $\mathbb{P}^2$, the expected count of the finite Quot scheme in arXiv:1610.04185 is its actual length. We also obtain a universality result for tautological integrals on the moduli space of stable pairs. Comment: 29 pages. In this new version, we extend one of our main theorems to more cases. Hence, we have changed the title. We also fix a mistake in Proposition 7.2 and one in the proof of Proposition 4.1 in the first version. Comments are welcome! |
| Databáze: | arXiv |
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