Seshadri stratifications and standard monomial theory

Inventiones mathematicae, vol. 234, pp. 489–572

Abstract

Abstract We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.

Authors 3

1. Rocco Chirivì

   University of Salento

   Affiliation as printed

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

2. Xin Fang corresponding Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Darstellungstheorie, RWTH Aachen University, Pontdriesch 10-16, 52062, Aachen, Germany

3. Peter Littelmann

   University of Cologne

   Affiliation as printed

   Department Mathematik/Informatik, Universität zu Köln, 50931, Cologne, Germany