Generic singularities and quasi-resolutions of Schubert varieties for the lineary group. (Q1408808)

The author determines explicitly the irreducible components of any Schubert variety \(\text{GL}_n(K)\) for any algebraically closed field \(K\) and describes the generic singularities along them. Similar results have been given by \textit{L. Manivel} [Int. Math. Res. Not. 2001, 849--871 (2001; Zbl 1023.14022)], \textit{S. Billey} and \textit{G. S. Warrington} [Trans. Am. Math. Soc. 355, 3915--3945 (2003; Zbl 1037.14020)], and \textit{C. Kassel, A. Lascoux} and \textit{C. Reutenauer} [J. Algebra 269, 74--108 (2003; Zbl 1032.14012)]. The methods of the present article are geometric and give a different and useful perspective of the field. Quasi-resolutions play an important role, and may be useful in computing Kazhdan-Lusztig polynomials for arbitrary polynomials. The proof builds heavily upon the results of \textit{A. Cortez} [Adv. Math. 178, 396--445 (2003; Zbl 1044.14026)].