MS Seminar (Mathematics - String Theory)

Speaker: Young-Hoon Kiem (Seoul National University)
Title: K-theoretic generalized Donaldson-Thomas invariants
Date (JST): Tue, Feb 18, 2020, 15:30 - 17:00
Place: Seminar Room A
Blackboard: (Blackboard talk)
Abstract: For the moduli of derived category objects or the partial desingularization of the moduli stack of semistable sheaves on a Calabi-Yau 3-fold, there seem to be 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 is too weak 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 (arXiv:1912.04966).