Explore: Schubert Varieties

{\displaystyle \mathbf {C} ^{n}} . Schubert varieties form one of the most important and best studied classes of singular algebraic varieties. A certain measure of

polynomials were related to the failure of local Poincaré duality for Schubert varieties. In Kazhdan & Lusztig (1980b) they reinterpreted this in terms of

enumerative geometry of algebraic varieties that are homogenous spaces of simple Lie groups. Even more generally, Schubert calculus is sometimes understood

S.; Ramanathan, A. (1985), "Projective normality of flag varieties and Schubert varieties", Inventiones Mathematicae, 79 (2): 217–224, Bibcode:1985InMat

points, lines, etc., using the intersection theory of Schubert varieties. Subvarieties of Schubert cells can also be used to parametrize simultaneous eigenvectors

that corresponds to the inclusion order on Schubert varieties. The Bruhat order on the Schubert varieties of a flag manifold or a Grassmannian was first

Franz Peter Schubert (/ˈʃuːbərt/; German: [fʁants ˈpeːtɐ ˈʃuːbɐt]; 31 January 1797 – 19 November 1828) was an Austrian composer of the late Classical and

describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of

combinatorics. She is known for her contributions on Schubert polynomials, singular loci of Schubert varieties, Kostant polynomials, and Kazhdan–Lusztig polynomials

ISBN 978-3-540-39274-3. Fulton, William; Pragacz, Piotr (1998). Schubert varieties and degeneracy loci. Lecture Notes in Mathematics. Vol. 1689. Springer-Verlag