Weighted interpolation from certain singular affine hypersurfaces

TL;DR

This paper demonstrates that square integrable holomorphic functions can be extended from specific singular hypersurfaces to entire functions, supporting a conjecture about the weight's curvature positivity.

Contribution

It proves extension results for holomorphic functions from singular hypersurfaces with implications for curvature positivity conjectures.

Findings

Extension of holomorphic functions from singular hypersurfaces

Supports conjecture on curvature positivity

Includes cases like normal crossing divisors

Abstract

We prove that square integrable holomorphic functions (with respect to a plurisubharmonic weight) can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to entire functions in affine space. This provides evidence for a conjecture regarding the positivity of the curvature of the weight under consideration.