Seminormal toric varieties
Fran\c{c}ois Bernard, Antoine Boivin

TL;DR
This paper introduces a combinatorial framework for seminormal toric varieties using fans with group data, expanding the class of toric varieties studied with simpler combinatorial tools.
Contribution
It provides a novel combinatorial description of seminormal toric varieties, generalizing normal varieties with simpler data than non-normal cases.
Findings
Provides a fan-based combinatorial model for seminormal toric varieties
Extends the class of toric varieties beyond normal cases
Simplifies the combinatorial data needed for non-normal toric varieties
Abstract
In this paper, we provide a combinatorial description of seminormal toric varieties. The corresponding combinatorial object is a fan equipped with a collection of groups assigned to each cone. This framework introduces a more general class of toric varieties than classical normal toric varieties, while having simpler combinatorial data compared to general non-normal toric varieties.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Polynomial and algebraic computation
