Combinatorial Seshadri stratifications on normal toric varieties

arXiv (Cornell University)

Abstract

We apply the theory of Seshadri stratifications to embedded toric varieties $X_P\subseteq \mathbb P(V)$ associated with a normal lattice polytope $P$. The approach presented here is purely combinatorial and completely independent of \cite{CFL}. In particular, we get a close connection between a certain class of triangulations of the polytope $P$, Seshadri stratifications of $X_P$ arising from torus orbit closures, and the associated degenerate semi-toric varieties. In the last section we show that the approach here and the one in \cite{CFL} produce the same quasi-valuations and hence the same degenerations of $X_P$.

Authors 4

1. Rocco Chirivì
2. Martina Costa Cesari Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University

   Affiliation as printed

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

3. Xin Fang Aachen Lehrstuhl für Algebra und Darstellungstheorie

   University of Cologne · RWTH Aachen University

   Affiliation as printed

   Department Mathematik/Informatik , Universität zu Köln , 50931 , Cologne , Ger - many

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

4. Peter Littelmann Aachen Lehrstuhl für Algebra und Darstellungstheorie

   RWTH Aachen University

   Affiliation as printed

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