When is a Schubert variety Gorenstein

By Alexander Woo, Alexander Yong. 2004

74 citations recorded by the source corpus.

Abstract A (normal) variety is Gorenstein if it is Cohen–Macaulay and its canonical sheaf is a line bundle. This property is a weakening of smoothness which implies that a variety behaves like a smooth one for various algebro-geometric purposes. We give a combinatorial characterization of which Schubert varieties are Gorenstein, using in part a new generalization of pattern avoidance. We also give an explicit description as a line bundle of the canonical sheaf of a Gorenstein Schubert variety.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/914c45140eb9a3e96c27c3d7c72a6b31cd831e80

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In Discrete Mathematics and Combinatorics

1. Einar Steingrímsson
2. Alexander Yong
3. Alexander Woo

In Geometry and Topology

1. Einar Steingrímsson
2. Alexander Yong
3. Alexander Woo

Citations in the corpus

• GOVERNING SINGULARITIES OF SCHUBERT VARIETIES (2006, background): “z21, z22, z23, z24, z25, z31, z32, z33, z34, z35, z41, z42, z43, z44, z45, z51, z52, z53, z54, z55]; n=5; -- graded diagonal term order on G -- below”
• Generalized permutation patterns - a short survey (2008, background): “It is also mentioned there that avoiding 2 1 3̄ 5 4 (and thus 2 14 3) is equivalent to avoiding 2 1 4 3 with Bruhat condition (1 ↔ 4) in the terminology of Woo and Yong, who conjectured [62] that a Schubert variety is locally factorial if and only if its associated permutation avoids these two patte”