Qregularity and tensor products of vector bundles on smooth quadric hypersurfaces

TL;DR

This paper proves a new regularity property for tensor products of sheaves and vector bundles on smooth quadric hypersurfaces, extending understanding of their cohomological behavior.

Contribution

It establishes that the tensor product of an m-Qregular sheaf and an l-Qregular vector bundle on a smooth quadric hypersurface is (m+l)-Qregular, a novel regularity result.

Findings

Tensor product of m-Qregular sheaf and l-Qregular bundle is (m+l)-Qregular.

Provides new insights into the cohomological properties of vector bundles on quadrics.

Extends regularity theory to tensor products on smooth quadric hypersurfaces.

Abstract

Let $\Q_n \subset \mathbb P^{n+1}$ be a smooth quadric hypersurface. Here we prove that the tensor product of an $m$-Qregular sheaf on $\Q_n$ and an $l$-Qregular vector bundle on $\Q_n$ is $(m+l)$-Qregular.