Seminormal toric varieties

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.