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Michail Savvas, PMA 9.166 : Reduction of stabilizers and Donaldson-Thomas invariants
Thursday, September 22, 2022, 03:30pm - 04:30pm
A typical feature in moduli theory is the presence of non-trivial automorphism groups (also known as stabilizers) of geometric objects, which makes it necessary to generalize the notion of a moduli space to that of a moduli stack in order to parametrize isomorphism classes of objects and their families. However, certain intersection-theoretic operations, such as integration, do not in general carry over to stacks. In this talk, I will explain a canonical procedure that eliminates the locus of points of a stack which have infinite stabilizers and produces a stack with finite stabilizers. The construction can be applied to moduli stacks of sheaves on Calabi-Yau threefolds and allows us to define new intersection-theoretic, generalized Donaldson-Thomas invariants counting these sheaves. Everything in this talk turns out to be the shadow of a corresponding phenomenon in derived algebraic geometry, giving a fully derived perspective on Donaldson-Thomas theory. Based on joint works with Young-Hoon Kiem, Jun Li and Jeroen Hekking.
Location: PMA 9.166

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