English

Hodge and Frobenius colevels of algebraic varieties

Algebraic Geometry 2025-04-23 v3 Number Theory

Abstract

We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over C\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.

Keywords

Cite

@article{arxiv.2309.16290,
  title  = {Hodge and Frobenius colevels of algebraic varieties},
  author = {Daqing Wan and Dingxin Zhang},
  journal= {arXiv preprint arXiv:2309.16290},
  year   = {2025}
}

Comments

25 pages. v3: Corrected the proof of Theorem 2.5. Final version