Nearly Toric Schubert Varieties of Type A
Mahir Bilen Can, Nestor Diaz Morera

TL;DR
This paper introduces nearly toric varieties, explores their properties within Schubert varieties of type A, and establishes combinatorial characterizations, counting formulas, and connections to Dyck paths.
Contribution
It defines nearly toric varieties in the context of Schubert varieties and provides combinatorial criteria and enumerations for smooth and singular cases.
Findings
Characterization of smooth nearly toric Schubert varieties
Enumeration formulas for nearly toric Schubert varieties
Connection established between Dyck paths and nearly toric Schubert varieties
Abstract
A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert varieties are found. Furthermore, the counts and generating series are determined. Additionally, a connection between Dyck paths and a certain family of nearly toric Schubert varieties is established.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory
