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# Pattern Avoidance and Rational Smoothness of Schubert Varieties

@inproceedings{Billey1998PatternAA, title={Pattern Avoidance and Rational Smoothness of Schubert Varieties}, author={Sara C. Billey}, year={1998} }

- Published 1998

Let w be an element of the Weyl group S n , and let X w be the Schubert variety associated to w in the ag manifold SL n (C)=B. Lakshmibai and Sandhya 12] showed that X w is smooth if and only if w avoids the patterns 4231 and 3412. Using two tests for rational smoothness due to Carrell and Peterson 2], we show that rational smoothness of X w is characterized by pattern avoidance for types B and C as well. A key step in the proof of this result is a sequence of rules for factoring the Poincar eâ€¦Â CONTINUE READING

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