Hodge and Frobenius colevels of algebraic varieties
arXiv:2309.16290
Abstract
We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over 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.
25 pages. v3: Corrected the proof of Theorem 2.5. Final version