Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces

Alexandre Minets ^[1]
1. [1] Institute of Science and Technology Austria, Austria
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00553-x
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Resumen
- 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}_C(\omega _C\oplus \mathcal {O}_C). In particular, we obtain an action of A\mathbf{Ha}_C^0 on the cohomology of Hilbert schemes of points on T^*C.