Friday May 3rd, 2024 | |
| Time: | 10:00 AM |
| Title: | Degeneration techniques in complex geometry |
| Speaker: | Roberto Albesiano, Stony Brook University |
| Abstract: | |
| In 2009, B. Berndtsson proved a theorem on the positivity of direct image bundles of\r\npositive line bundles. Berndtsson’s theorem has been successfully used to give radically\r\nnew proofs of some fundamental theorems in the part of complex geometry often referred\r\nto as $L^2$ methods; proofs that are based on the monotonicity of certain degenerations into\r\nsituations in which the results are obvious, and that reveal an unexpected underlying\r\nconvexity. Among these is a proof of the $L^2$ extension with sharp estimates. As a step\r\ntowards determining how much of the classical $L^2$ theory can be recovered by this\r\ntechnique, we will present a new proof of a Skoda-type $L^2$ division theorem. | |