Dror Varolin, Stony Brook University
Extending sections of Holomorphic Vector Bundles
In 1987 Ohsawa and Takegoshi published their fundamental result on L2 extension of holomorphic functions. It did not take long for this result to be generalized to sections of holomorphic line bundles, and a spectacular array of applications appeared in a number of areas of complex analytic and algebraic geometry. By contrast, the L2 Extension of sections of holomorphic vector bundles has been much less considered. In particular, until recently optimal positivity conditions were not totally understood. In this talk I will present a result about L2 Extension in the higher rank case, and also an example showing that this type of positivity is optimal. I will also discuss the relevance to a question about deformation of spaces of holomorphic sections.
MC 5417