scholarly journals Tangent cones to Schubert varieties in types A, B and C

2016 ◽  
Vol 465 ◽  
pp. 259-286 ◽  
Author(s):  
Mikhail A. Bochkarev ◽  
Mikhail V. Ignatyev ◽  
Aleksandr A. Shevchenko
Keyword(s):  
Schubert Varieties ◽  
Tangent Cones

scholarly journals On tangent cones to Schubert varieties in type E

2020 ◽  
Vol 28 (2) ◽  
pp. 179-197
Author(s):  
Mikhail V. Ignatyev ◽  
Aleksandr A. Shevchenko
Keyword(s):  
Algebraic Group ◽  
Weyl Group ◽  
Tangent Space ◽  
Borel Subgroup ◽  
Flag Variety ◽  
Neutral Point ◽  
Schubert Varieties ◽  
Tangent Cones ◽  
Good Pair

AbstractWe consider tangent cones to Schubert subvarieties of the flag variety G/B, where B is a Borel subgroup of a reductive complex algebraic group G of type E6, E7 or E8. We prove that if w1 and w2 form a good pair of involutions in the Weyl group W of G then the tangent cones Cw1 and Cw2 to the corresponding Schubert subvarieties of G/B do not coincide as subschemes of the tangent space to G/B at the neutral point.

Tangent cones of schubert varieties for A n of lower rank

2013 ◽  
Vol 188 (5) ◽  
pp. 596-600 ◽  
Author(s):  
D. Yu. Eliseev ◽  
A. N. Panov
Keyword(s):  
Schubert Varieties ◽  
Tangent Cones ◽  
Lower Rank

scholarly journals On Tangent Cones of Schubert Varieties

2017 ◽  
Vol 3 (4) ◽  
pp. 451-482
Author(s):  
Dmitry Fuchs ◽  
Alexandre Kirillov ◽  
Sophie Morier-Genoud ◽  
Valentin Ovsienko
Keyword(s):  
Schubert Varieties ◽  
Tangent Cones

scholarly journals Singularities of Schubert varieties, tangent cones and Bruhat graphs

2006 ◽  
Vol 128 (1) ◽  
pp. 121-138 ◽  
Author(s):  
James B. Carrell ◽  
Jochen Kuttler
Keyword(s):  
Schubert Varieties ◽  
Tangent Cones

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

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.

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.

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