Pure and Applied Mathematics Quarterly

Volume 20 (2024)

Number 3

Special Issue in Honor of Claudio Procesi

Guest Editors: Luca Migliorini, Paolo Papi, and Mario Salvetti

On normal Seshadri stratifications

Pages: 1097 – 1139

DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n3.a3

Authors

Rocco Chirivì (Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy)

Xin Fang (Lehrstuhl für Algebra und Darstellungstheorie, RWTH Aachen University, Aachen, Germany)

Peter Littelmann (Department Mathematik/Informatik, Universität zu Köln, Germany)

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 Gröbner 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.

Keywords

Seshadri stratification, standard monomial theory, semitoric degeneration, normal toric varieties

2010 Mathematics Subject Classification

13F50, 14M25

Received 27 June 2022

Received revised 10 March 2023

Accepted 11 April 2023

Published 15 May 2024