arXiv subjects

Martina Costa Cesari

Publications and source records attributed to Martina Costa Cesari.

4 recordsLinked to original sources

arXiv2026

Higher rank Gelfand-Kapranov-Zelevinsky fans

We define and study the higher rank GKZ-fans of point configurations, serving as the set of discrete and homogeneous quasi-valuations on the homogeneous coordinate ring of the associated toric variety, where the rank one cases coincide with the usual GKZ-fans. Such a quasi-valuation is then used to degenerate the toric variety flatly to a reduced union of toric varieties, which encodes the polytopal subdivision arising from the point in the higher rank GKZ-fan.

math.AG↗

arXiv2026

Lecture hall polytopes and Lakshmibai-Seshadri paths

Using a bijection between the lattice points in a lecture hall polytope and Lakshimibai-Seshadri (L-S) paths, we prove the Koszul property of lecture hall polytopes in complete generality, and give new proofs for their Integral Decomposition Property and for a criterion on Gorenstein property.

math.CO↗

arXiv2025

Combinatorial Seshadri stratifications on normal toric varieties

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 $X_P$.

math.AG↗

arXiv2022

Jordan classes and Lusztig strata in disconnected reductive groups

Let $G$ be a non-connected reductive algebraic group over an algebraically closed field $\mathbb{K}$ and let $D$ be a connected component of $G$. We investigate Jordan classes of $D$ and we obtain a description of the regular part of the closure of a Jordan class in terms of induction of $G^{\circ}$-orbits. We use this result to show that Lusztig strata in a non-connected reductive algebraic group are locally closed.

math.RT↗