A degeneration approach to Skoda's L2 division theorem
Speaker:
Roberto Albesiano (Waterloo)
Date and Time:
Thursday, November 7, 2024 - 2:00pm to 3:00pm
Location:
Fields Institute, Room 309, Stewart Library
Abstract:
A classical problem in complex geometry is to decide when a given holomorphic section is in the ideal generated by a fixed set of holomorphic sections, i.e. when it is a linear combination of the generators with holomorphic coefficients. In 1972, H. Skoda proved a theorem addressing this question and giving L2 bounds on the solution with minimal L2 norm. I will sketch a different proof of a Skoda-type theorem inspired by a degeneration argument of B. Berndtsson and L. Lempert. In particular, we will see how to obtain the L2 bounds by deforming a weight on the space parametrizing all linear combinations to single out the one witnessing the ideal membership property.