The L2-Stokes Theorem on Complex Varieties and Dolbeault Cohomology

Jean Ruppenthal (BUW)

Nov 21. 2023, 15:00 — 15:50

Let X be a singular complex space. Roughly speaking, by definition, one says that the L2-Stokes-Theorem holds on X for the exterior derivative d or for the $\overline{\partial}$-operator, respectively, if partial integration is possible with respect to these operators on L2-forms, i.e., the singular set should be negligible in a certain sense. It is conjectured, that the L2-Stokes-Theorem holds for d on projective varieties, and it is known to fail in general for $\overline{\partial}$. In this talk, we will discuss the state of the art and present an idea of how to overcome the problem for the $\overline{\partial}$-operator.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Analysis and Geometry in Several Complex Variables (Workshop)
Peter Ebenfelt (UC San Diego)
Purvi Gupta (IIS Bengalore)
Bernhard Lamel (U of Vienna)
Nordine Mir (Texas A&M U at Qatar)