The uniqueness theorem for Gysin coherent characteristic classes of singular spaces
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of a recursive nature terminating on genera of explicit characteristic subvarieties that we construct.
Markus Banagl, Dominik J. Wrazidlo
wiley +1 more source
Presenting the cohomology of a Schubert variety: Proof of the minimality conjecture
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract A minimal presentation of the cohomology ring of the flag manifold GLn/B$GL_n/B$ was given in A. Borel (1953). This presentation was extended by E. Akyildiz–A. Lascoux–P. Pragacz (1992) to a nonminimal one for all Schubert varieties. Work of V. Gasharov–V.
Avery St. Dizier, Alexander Yong
wiley +1 more source
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians [PDF]
, 2014 We investigate double transitivity of Galois groups in the classical Schubert calculus on Grassmannians. We show that all Schubert problems on Grassmannians of 2- and 3-planes have doubly transitive Galois groups, as do all Schubert problems involving ...
Sottile, Frank, White, Jacob
core
Manifolds of low dimension with trivial canonical bundle in Grassmannians
, 2017 We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians.
Benedetti, Vladimiro
core +1 more source
Integral homology of real isotropic and odd orthogonal Grassmannians
, 2020 We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic Grassmannians.
Lambert, Jordan, Rabelo, Lonardo
core
Mutations of puzzles and equivariant cohomology of two-step flag varieties [PDF]
, 2014 We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure ...
Buch, Anders Skovsted
core
Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
, 1997 We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space.
Sottile, Frank
core +5 more sources
Schubert puzzles and integrability I: invariant trilinear forms
, 2020 The puzzle rules for computing Schubert calculus on $d$-step flag manifolds, proven in [Knutson Tao 2003] for $1$-step, in [Buch Kresch Purbhoo Tamvakis 2016] for $2$-step, and conjectured in [Coskun Vakil 2009] for $3$-step, lead to vector ...
Knutson, Allen, Zinn-Justin, Paul
core
The mirror conjecture for minuscule flag varieties
, 2017 We prove Rietsch's mirror conjecture that the Dubrovin quantum connection for minuscule flag varieties is isomorphic to the character D-module of the Berenstein-Kazhdan geometric crystal.
Lam, Thomas, Templier, Nicolas
core
An algorithm for computing Schubert varieties of best fit with applications. [PDF]
Front Artif Intell, 2023 Karimov K, Kirby M, Peterson C.
europepmc +1 more source