A Converse to the Skoda $L^2$ division theorem II

Abstract

We prove a converse to the original Skoda $L^2$ division theorem, asserting that Skoda $L^2$ division estimates for a single nonzero holomorphic function force the weight to be plurisubharmonic. In addition, we establish corresponding results for higher-rank quotient bundles. Finally, we derive an optimal $L^2$ extension theorem directly from the division estimates.

arXiv comment28 pages, comments welcome!