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Which Schubert varieties are Gorenstein?
Algebra & Discrete Mathematics| Speaker: | Alexander Woo, UC Berkeley |
| Location: | 693 Kerr |
| Start time: | Fri, Jan 28 2005, 12:10PM |
Description
We give a new combinatorial characterization for which
Schubert varieties (for SL(n)) are Gorenstein. Gorenstein-ness is a
technical algebro-geometric condition which is a weakening of
smoothness. In analogy with the now classic result of Lakshmibai and
Sandhya characterizing smooth Schubert varieties in terms of pattern
avoidance conditions, our results are in terms of a generalization of
pattern avoidance which I will describe. When combined with other
geometric results, our results are further evidence that the
singularity structure of Schubert varieties is not too complicated.
If time permits I will also describe some open problems and ongoing
work. This is a joint project with Alexander Yong.