English

Sharp volume and multiplicity bounds for Fano simplices

Combinatorics 2023-08-25 v1 Algebraic Geometry

Abstract

We present sharp upper bounds on the volume, Mahler volume and multiplicity for Fano simplices depending on the dimension and Gorenstein index. These bounds rely on the interplay between lattice simplices and unit fraction partitions. Moreover, we present an efficient procedure for explicitly classifying Fano simplicies of any dimension and Gorenstein index and we carry out the classification up to dimension four for various Gorenstein indices.

Keywords

Cite

@article{arxiv.2308.12719,
  title  = {Sharp volume and multiplicity bounds for Fano simplices},
  author = {Andreas Bäuerle},
  journal= {arXiv preprint arXiv:2308.12719},
  year   = {2023}
}

Comments

27 pages. Comments welcome

R2 v1 2026-06-28T12:03:22.526Z