Analytic inversion of adjunction: L^2 extension theorems with gain

TL;DR

This paper develops new weighted L^2 extension theorems for holomorphic forms from hypersurfaces, introducing denominators that optimize extension weights, advancing the understanding of analytic inversion of adjunction.

Contribution

It introduces novel weighted L^2 extension results with specific denominators, enhancing the analytic tools for extending holomorphic forms from hypersurfaces.

Findings

Established new weighted L^2 extension theorems

Introduced denominators related to divisors for optimal weights

Provided examples illustrating the application of denominators

Abstract

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.