Combinatorial Seshadri stratifications on normal toric varieties
Rocco Chiriv\`i, Martina Costa Cesari, Xin Fang, Peter Littelmann

TL;DR
This paper introduces a purely combinatorial approach to Seshadri stratifications on normal toric varieties, linking polytope triangulations, orbit closures, and degenerations, and shows equivalence with previous methods.
Contribution
It presents a new combinatorial framework for Seshadri stratifications on toric varieties, independent of prior work, connecting triangulations, stratifications, and degenerations.
Findings
Establishes a connection between polytope triangulations and Seshadri stratifications.
Shows the combinatorial approach yields the same degenerations as previous methods.
Provides a new perspective on degenerations of toric varieties via combinatorics.
Abstract
We apply the theory of Seshadri stratifications to embedded toric varieties associated with a normal lattice polytope . 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 , Seshadri stratifications of 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 .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Polynomial and algebraic computation
