On normal Seshadri stratifications

TL;DR

This paper explores the concept of normal Seshadri stratifications, showing how they enable lifting Gr"obner bases to the original variety and discussing implications for algebraic properties like Koszulness and Gorenstein conditions.

Contribution

It establishes the connection between normal Seshadri stratifications and the lifting of Gr"obner bases, with applications to algebraic properties and relations to LS-algebras.

Findings

Gr"obner basis of semi-toric variety can be lifted to the embedded variety.

Normal Seshadri stratifications facilitate understanding of algebraic properties.

Relations between LS-algebras and Seshadri stratifications are characterized.

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.