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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
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
A Claudio, che ci mostra la via
Received 27 June 2022
Received revised 10 March 2023
Accepted 11 April 2023
Published 15 May 2024