When is a Schubert variety Gorenstein?

Alexander Woo, Alexander Yong

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)205-220
Number of pages16
JournalAdvances in Mathematics
Issue number1
StatePublished - Dec 1 2006
Externally publishedYes


  • Bruhat-restricted pattern avoidance
  • Gorenstein variety
  • Singularities of Schubert varieties

ASJC Scopus subject areas

  • General Mathematics


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