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arXiv · 1310.6473

On the F-rationality and cohomological properties of matrix Schubert varieties

Jen-Chieh Hsiao
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Abstract

We characterize complete intersection matrix Schubert varieties, generalizing the classical result on one-sided ladder determinantal varieties. We also give a new proof of the F-rationality of matrix Schubert varieties. Although it is known that such varieties are F-regular (hence F-rational) by the global F-regularity of Schubert varieties, our proof is of independent interest since it does not require the Bott-Samelson resolution. As a consequence, this provides an alternative proof of the classical fact that Schubert varieties in flag varieties are normal and have rational singularities.

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Jen-Chieh Hsiao. 2013-10-24. On the F-rationality and cohomological properties of matrix Schubert varieties. https://arxiv.org/abs/1310.6473

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