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K-theoretic generalized Donaldson-Thomas invariants

Banff International Research Station for Mathematical Innovation and Discovery

For the moduli of derived category objects or the partial desingularizations of the moduli stack of semistable sheaves on Calabi-Yau 3-folds, there are no perfect obstruction theories but only semi-perfect obstruction theories. While a semi-perfect obstruction theory is sufficient for the construction of virtual cycles in Chow groups, it seems insufficient for virtual structure sheaves. In this talk, I will introduce the notion of an almost perfect obstruction theory, which lies in between a semi-perfect obstruction theory and an honest perfect obstruction theory. I will show that an almost perfect obstruction theory enables us to construct the virtual structure sheaf and hence K-theoretic virtual invariants. Examples of DM stacks with almost perfect obstruction theories include the Inaba-Lieblich moduli spaces of simple gluable perfect complexes and the partial desingularizations of moduli stacks of semistable sheaves on Calabi-Yau 3-folds. We thus obtain K-theoretic Donaldson-Thomas invariants of derived category objects and K-theoretic generalized Donaldson-Thomas invariants. Based on a joint work with Michail Savvas.

Mathematics; Algebraic geometry

video/mp4

Author affiliation: Seoul National University

2020-05-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74505

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/