TL;DR
This paper investigates the non-Gorenstein loci of normal toric varieties and Hibi rings, providing combinatorial descriptions and applying these findings to secant varieties of Segre varieties.
Contribution
It offers a combinatorial characterization of non-Gorenstein loci in Hibi rings and computes their dimensions in secant varieties, extending understanding beyond toric cases.
Findings
Combinatorial description of non-Gorenstein loci in Hibi rings
Dimension calculations for non-Gorenstein loci of secant varieties
Extension of non-Gorenstein locus analysis to non-toric varieties
Abstract
We describe the non-Gorenstein loci of normal toric varieties. In the case of Hibi rings a combinatorial description is provided in terms of the underlying partially ordered set. As a non-toric application we compute the dimensions of the non-Gorenstein loci of the first secant variety of Segre varieties.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics