## Illinois Journal of Mathematics

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

Jen-Chieh Hsiao

#### 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 of Schubert varieties. As a consequence, this provides an alternative proof of the classical fact that Schubert varieties in flag varieties are normal and have rational singularities.

#### Article information

Source
Illinois J. Math., Volume 57, Number 1 (2013), 1-15.

Dates
First available in Project Euclid: 23 June 2014

https://projecteuclid.org/euclid.ijm/1403534482

Digital Object Identifier
doi:10.1215/ijm/1403534482

Mathematical Reviews number (MathSciNet)
MR3224557

Zentralblatt MATH identifier
1312.14117

#### Citation

Hsiao, Jen-Chieh. On the $F$-rationality and cohomological properties of matrix Schubert varieties. Illinois J. Math. 57 (2013), no. 1, 1--15. doi:10.1215/ijm/1403534482. https://projecteuclid.org/euclid.ijm/1403534482

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