Hodge and Frobenius colevels of algebraic varieties

TL;DR

This paper establishes improved lower bounds for Hodge and Frobenius colevels of algebraic varieties, linking these bounds to the variety's dimension and defining equations, and addresses a question by Esnault and the first author.

Contribution

It introduces new bounds for colevels of algebraic varieties over complex numbers and finite fields, advancing understanding in algebraic geometry.

Findings

Derived new lower bounds for colevels in all cohomological degrees

Expressed bounds in terms of variety dimension and multi-degrees

Provided an improved positive answer to a previously posed question

Abstract

We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over $\mathbf{C}$ or over a finite field) in all cohomological degrees. These bounds are expressed in terms of the dimension of the variety and multi-degrees of its defining equations. Our results lead to an enhanced positive answer to a question raised by Esnault and the first author.