Regularity and Segre-Veronese embeddings

TL;DR

This paper investigates the regularity of sheaves from Segre-Veronese embeddings, providing explicit formulas and demonstrating subadditivity, with applications to Tate resolutions.

Contribution

It introduces explicit regularity formulas for sheaves from Segre-Veronese embeddings and proves their subadditivity, advancing understanding of their algebraic properties.

Findings

Explicit regularity formulas derived

Regularity shown to be subadditive

Applications to Tate resolutions explored

Abstract

This paper studies the regularity of certain coherent sheaves that arise naturally from Segre-Veronese embeddings of a product of projective spaces. We give an explicit formula for the regularity of these sheaves and show that their regularity is subadditive. We then apply our results to study the Tate resolutions of these sheaves.