Weighted Castelnuovo-Mumford Regularity and Weighted Global Generation

TL;DR

This paper introduces a new concept of Castelnuovo-Mumford regularity tailored for weighted projective spaces, expanding the tools available for algebraic geometry in weighted contexts.

Contribution

It defines and investigates a weighted version of Castelnuovo-Mumford regularity, a fundamental invariant in algebraic geometry, for the setting of weighted projective spaces.

Findings

Established properties of the weighted regularity.

Connected weighted regularity to global generation.

Provided examples illustrating the concept.

Abstract

Weighted Castelnuovo-Mumford Regularity and Weighted Global GenerationWe introduce and study a notion of Castelnuovo-Mumford regularity suitable for weighted projective spaces.