When is a Schubert variety Gorenstein?

• Autores: Alexander Woo, Alexander Yong
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 1, 2006, págs. 205-220
• Idioma: inglés
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• Resumen

  • 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.