Combinatorial Seshadri stratifications on normal toric varieties

2025/01/27 by Chirivì, Rocco, Cesari, Martina Costa, Fang, Xin +1
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.16161

Abstract

We apply the theory of Seshadri stratifications to embedded toric varieties X_P⊆ \mathbb P(V) associated with a normal lattice polytope P. The approach presented here is purely combinatorial and completely independent of \citeCFL. 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 \citeCFL produce the same quasi-valuations and hence the same degenerations of X_P.

Related

• On normal Seshadri stratifications
• Toric Geometry and the Semple-Nash modification
• Combinatorics and Quotients of Toric Varieties
• Stratification of Projection Maps From Toric Varieties
• Selected topics on Toric Varieties