On normal Seshadri stratifications
Algebraic Geometry
2025-09-03 v2 Commutative Algebra
Abstract
The existence of a Seshadri stratification on an embedded projective variety provides a flat degeneration of the variety to a union of projective toric varieties, called a semi-toric variety. Such a stratification is said to be normal when each irreducible component of the semi-toric variety is a normal toric variety. In this case, we show that a Gr\"obner basis of the defining ideal of the semi-toric variety can be lifted to define the embedded projective variety. Applications to Koszul and Gorenstein properties are discussed. Relations between LS-algebras and certain Seshadri stratifications are studied.
Cite
@article{arxiv.2206.13171,
title = {On normal Seshadri stratifications},
author = {Rocco Chirivì and Xin Fang and Peter Littelmann},
journal= {arXiv preprint arXiv:2206.13171},
year = {2025}
}
Comments
v2: 33 pages, updated the publish version, a new Section 5 on the relations to LS-algebras is added