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

S. Minets, Selecta Mathematica, New Series 26 (2020).

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Journal Article | Published | English
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Abstract
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 AHa0C 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 AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C.
Publishing Year
Date Published
2020-04-15
Journal Title
Selecta Mathematica, New Series
Volume
26
Issue
2
Article Number
30
ISSN
eISSN
IST-REx-ID

Cite this

Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2). doi:10.1007/s00029-020-00553-x
Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series, 26(2). https://doi.org/10.1007/s00029-020-00553-x
Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series 26, no. 2 (2020). https://doi.org/10.1007/s00029-020-00553-x.
S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol. 26, no. 2, 2020.
Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2).
Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol. 26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x.
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