# Fiber invariants of projective morphisms and regularity of powers of ideals

## TL;DR

This paper introduces a new invariant for coherent sheaves over projective morphisms, which helps estimate the stability of regularity and a*-invariant of ideal powers, advancing understanding of their cohomological behavior.

## Contribution

The paper defines a novel invariant that links sheaf cohomology behavior to the stability of regularity and a*-invariant in powers of ideals, providing new tools for algebraic geometry.

## Key findings

- Invariant controls sheaf cohomology transfer
- Estimates stability indexes of regularity
- Provides bounds for a*-invariant of ideal powers

## Abstract

We introduce an invariant, associated to a coherent sheaf over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism. We then use this invariant to estimate the stability indexes of the regularity and a*-invariant of powers of homogeneous ideals.