Frobenius Splitting of Schubert Varieties and Linear Syzygies

1994 ◽  
Vol 116 (6) ◽  
pp. 1569 ◽  
Author(s):  
S. P. Inamdar ◽  
V. B. Mehta
Keyword(s):  
Schubert Varieties ◽  
Frobenius Splitting ◽  
Linear Syzygies

scholarly journals On a conjecture of Pappas and Rapoport about the standard local model for GL_d

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinakar Muthiah ◽  
Alex Weekes ◽  
Oded Yacobi
Keyword(s):  
Type A ◽  
Positive Answer ◽  
Local Model ◽  
Schubert Varieties ◽  
Shimura Varieties ◽  
Local Models ◽  
Full Generality ◽  
Frobenius Splitting ◽  
Affine Grassmannians ◽  
Main Ideas

AbstractIn their study of local models of Shimura varieties for totally ramified extensions, Pappas and Rapoport posed a conjecture about the reducedness of a certain subscheme of {n\times n} matrices. We give a positive answer to their conjecture in full generality. Our main ideas follow naturally from two of our previous works. The first is our proof of a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman on the equations defining type A affine Grassmannians. The second is the work of the first two authors and Kamnitzer on affine Grassmannian slices and their reduced scheme structure. We also present a version of our argument that is almost completely elementary: the only non-elementary ingredient is the Frobenius splitting of Schubert varieties.

Frobenius Splitting and Cohomology Vanishing for Schubert Varieties

1985 ◽  
Vol 122 (1) ◽  
pp. 27 ◽  
Author(s):  
V. B. Mehta ◽  
A. Ramanathan
Keyword(s):  
Schubert Varieties ◽  
Frobenius Splitting

scholarly journals Frobenius splitting of Schubert varieties of semi-infinite flag manifolds

2021 ◽  
Vol 9 ◽  
Author(s):  
Syu Kato
Keyword(s):  
Positive Characteristic ◽  
Formal Model ◽  
Flag Manifold ◽  
Schubert Varieties ◽  
Flag Manifolds ◽  
Line Bundles ◽  
Closed Field ◽  
Flag Varieties ◽  
Fixed Degree ◽  
Frobenius Splitting

Abstract 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. We show that the formal model of a semi-infinite flag variety admits a unique nice (ind-)scheme structure, its projective coordinate ring has a $\mathbb {Z}$ -model and it admits a Frobenius splitting compatible with the boundaries and opposite cells in positive characteristic. This establishes the normality of the Schubert varieties of the quasi-map space with a fixed degree (instead of their limits proved in [K, Math. Ann. 371 no.2 (2018)]) when $\mathsf {char}\, {\mathbb K} =0$ or $\gg 0$ , and the higher-cohomology vanishing of their nef line bundles in arbitrary characteristic $\neq 2$ . Some particular cases of these results play crucial roles in our proof [47] of a conjecture by Lam, Li, Mihalcea and Shimozono [60] that describes an isomorphism between affine and quantum K-groups of a flag manifold.

scholarly journals Frobenius splitting and geometry of G-Schubert varieties

2008 ◽  
Vol 219 (5) ◽  
pp. 1469-1512 ◽  
Author(s):  
Xuhua He ◽  
Jesper Funch Thomsen
Keyword(s):  
Schubert Varieties ◽  
Frobenius Splitting

scholarly journals Frobenius Splitting of Thick Flag Manifolds of Kac–Moody Algebras

2018 ◽  
Vol 2020 (17) ◽  
pp. 5401-5427 ◽  
Author(s):  
Syu Kato
Keyword(s):  
Line Bundle ◽  
Schubert Variety ◽  
Flag Manifold ◽  
Schubert Varieties ◽  
Flag Manifolds ◽  
Flag Varieties ◽  
Moody Algebra ◽  
Frobenius Splitting ◽  
Projective Normality ◽  
Plücker Relations

Abstract We explain that the Plücker relations provide the defining equations of the thick flag manifold associated to a Kac–Moody algebra. This naturally transplants the result of Kumar–Mathieu–Schwede about the Frobenius splitting of thin flag varieties to the thick case. As a consequence, we provide a description of the space of global sections of a line bundle of a thick Schubert variety as conjectured in Kashiwara–Shimozono [13]. This also yields the existence of a compatible basis of thick Demazure modules and the projective normality of the thick Schubert varieties.

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

On Schubert varieties in the flag manifold of Sl(n,?)

1987 ◽  
Vol 276 (2) ◽  
pp. 205-224 ◽  
Author(s):  
Kevin M. Ryan
Keyword(s):  
Flag Manifold ◽  
Schubert Varieties
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