Cohomology of Smooth Schubert Varieties in Partial Flag Manifolds
Journal of the London Mathematical Society, 2002 Vesselin Gasharov, Victor Reiner
exaly +2 more sources
Generalized juggling patterns, quiver Grassmannians and affine flag varieties [PDF]
Mathematische Zeitschrift, 2023 The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties.
E. Feigin, M. Lanini, Alexander Pütz
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Symplectic Conditions on Grassmannian, Flag, and Schubert Varieties [PDF]
Communications in Mathematical Research, 2022 In this paper, a description of the set-theoretical defining equations of symplectic (type C) Grassmannian/flag/Schubert varieties in corresponding (type A) algebraic varieties is given as linear polynomials in Pl$\ddot{u}$cker coordinates, and it is ...
Jiajun Xu, Guanglian Zhang
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On the cohomology rings of real flag manifolds: Schubert cycles [PDF]
Mathematische Annalen, 2019 We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the Schubert cells.
Á. Matszangosz
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Bioriented flags and resolutions of Schubert varieties [PDF]
Mathematische Nachrichten, 2018 We use incidence relations running in two directions in order to construct a Kempf–Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian.
Daniel Cibotaru
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The isomorphism problem for cominuscule Schubert varieties [PDF]
Selecta Mathematica, 2023 Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These labeled posets generalize Young diagrams.
Edward Richmond +2 more
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The AS–Cohen–Macaulay property for quantum flag manifolds of minuscule weight [PDF]
, 2007 It is shown that quantum homogeneous coordinate rings of generalised flag manifolds corresponding to minuscule weights, their Schubert varieties, big cells, and determinantal varieties are AS–Cohen–Macaulay. The main ingredient in the proof is the notion
S. Kolb
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Frobenius splitting of Schubert varieties of semi-infinite flag manifolds [PDF]
Forum of Mathematics, Pi, 2018 We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field ${\mathbb K}$ of characteristic $\neq 2$ from scratch.
Syu Kato
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Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1 [PDF]
Acta Mathematica Sinica. English series, 2017 Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of ...
Shin-young Kim, Kyeong-Dong Park
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Semi-infinite Schubert varieties and quantum K-theory of flag manifolds [PDF]
, 2011 Let g be a semi-simple Lie algebra. In this paper we study the spaces of based quasi-maps from the projective line P^1 to the flag variety of g (it is well-known that their singularities are supposed to model the singularities of the so called semi ...
A. Braverman, M. Finkelberg
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