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Non-commutative Hilbert schemes and Hall algebras

Algebraic Geometry and Number Theory Seminar

Date: Thursday, April 20, 2023 13:00 - 15:00
Speaker: Sergey Mozgovoy (Trinity College Dublin)
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series: Mathematics and CS Seminar
Host: Tamas Hausel
Contact: Birgit Oosthuizen-Noczil

Non-commutative Hilbert schemes are smooth moduli spaces of framed quiver representations. For example, for a quiver with one vertex and no arrows they can be identified with Grassmannians and for a quiver of type $A_n$ they can be identified with flag varieties. The non-commutative Hilbert schemes possess cellular decompositions, giving rise to non-canonical bases of cohomology groups. In this talk I will discuss another basis of cohomology groups, consisting of products of Chern classes of universal vector bundles over nc-Hilbert schemes. This basis is obtained by interpreting cohomology of nc-Hilbert schemes as a module over the cohomological Hall algebra of the quiver.


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