Which Schubert varieties are Gorenstein?Algebra & Discrete Mathematics
|Alexander Woo, UC Berkeley
|Fri, Jan 28 2005, 12:10PM
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.