| Autor: |
Arbesfeld, Noah, Johnson, Drew, Lim, Woonam, Oprea, Dragos, Pandharipande, Rahul |
| Rok vydání: |
2020 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.geomphys.2021.104154 |
| Popis: |
We study virtual invariants of Quot schemes parametrizing quotients of dimension at most 1 of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecture that the generating series of virtual K-theoretic invariants are given by rational functions. We prove rationality for several geometries including punctual quotients for all smooth projective surfaces and dimension 1 quotients for surfaces X with p_g>0. We also show that the generating series of virtual cobordism classes can be irrational. Given a K-theory class on X of rank r, we associate natural series of virtual Segre and Verlinde numbers. We show that the Segre and Verlinde series match in the following three cases: Quot schemes of dimension 0 quotients, Hilbert schemes of points and curves over surfaces with p_g>0, Quot schemes of minimal elliptic surfaces for quotients supported on fiber classes. Moreover, for punctual quotients of the trivial sheaf of rank N, we prove a new symmetry of the Segre/Verlinde series exchanging r and N. The Segre/Verlinde statements have analogues for punctual Quot schemes over curves. |
| Databáze: |
arXiv |
| Externí odkaz: |
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