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When is a Schubert variety Gorenstein?

Alexander Woo·Alexander Yong
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Abstract

A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. We determine which Schubert varieties are Gorenstein in terms of a combinatorial characterization using generalized pattern avoidance conditions. We also give an explicit description as a line bundle of the canonical sheaf of a Gorenstein Schubert variety.

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Alexander Woo, Alexander Yong. 2005-11-21. When is a Schubert variety Gorenstein?. https://arxiv.org/abs/math/0409490

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