Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
| Autor: | Minets, Alexandre |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Sel. Math. New Ser. 26, 30 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00029-020-00553-x |
| Popis: | For any free oriented Borel-Moore homology theory $A$, we construct an associative product on the $A$-theory of the stack of Higgs torsion sheaves over a projective curve $C$. We show that the resulting algebra $A\mathbf{Ha}_C^0$ admits a natural shuffle presentation, and prove it is faithful when $A$ is replaced with usual Borel-Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose $A$-theory admits an $A\mathbf{Ha}_C^0$-action. These triples can be interpreted as certain sheaves on $\mathbb P(T^*C)$. In particular, we obtain an action of $A\mathbf{Ha}_C^0$ on the cohomology of Hilbert schemes of points on $T^*C$. Comment: 51 pages, completely rewritten section 7 |
| Databáze: | arXiv |
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