报告题目：Dolbeault superconnections on complex-analytic manifolds

报告时间：2025-03-13   16:00-17:00

报  告 人 ：Alexey Bondal

Leading Researcher (Steklov Mathematical Institute in Moscow)

Director (Center for Pure Mathematics, Moscow Institute for Physics and Technology )

Senior Fellow (Kavli Institute for the Physics and Mathematics of the Universe)

报告地点：雷军科技楼六楼报告厅（644）

Abstract：We will discuss various versions of the derived category of coherent sheaves on compact complex-analytic manifolds and dg-enhancement of the suitable version of the category via Dolbeault superconnections. This enhancement allows us to define Chern and Bott-Chern classes of objects of the category, in particular of coherent sheaves. Also it allows us to construct the complex-analytic moduli spaces of objects in the category. The theory is generalized to non-compact complex-analytic manifolds, where one should consider the category of restricted objects of the derived category. We will analyze when this notion is homological.