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Schubert Calculus on the Arithmetic Grassmannian
Arithmetic Grassmannian Schubert Calculus
2015/12/17
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of
the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
STANDARD CONJECTURES FOR THE ARITHMETIC GRASSMANNIAN G(2; N) AND RACAH POLYNOMIALS
STANDARD CONJECTURES RACAH POLYNOMIALS
2015/12/17
We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G(2; N) parametrizing
lines in projective space, for the natural arithmetic Lefschetz operator de ned via t...
QUANTUM COHOMOLOGY OF THE LAGRANGIAN GRASSMANNIAN
LAGRANGIAN GRASSMANNIAN QUANTUM COHOMOLOGY
2015/12/17
Let V be a symplectic vector space and LG be the Lagrangian
Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH¤(LG) ...
Window shifts, flop equivalences and Grassmannian twists
Window shifts flop equivalences Grassmannian twists Algebraic Geometry
2012/6/14
We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seid...
Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
Sigma models Mathematical Physics Holomorphic solutions
2012/4/18
We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also...
Parallel submanifolds of the real 2-Grassmannian
Parallel submanifolds real 2-Grassmannian Differential Geometry
2011/9/22
Abstract: We classify parallel submanifolds of the Grassmannian $\rmG^+_2(\R^{n+2})$ which parameterizes the oriented 2-planes of the Euclidean space $\R^{n+2}$. Our main result states that every comp...
Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Quantum grassmannians quantum Richardson varieties quantum toric varieties straightening laws standard monomials
2011/8/29
Abstract: In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum anal...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
KP solitons and total positivity for the Grassmannian
KP solitons total positivity Grassmannian
2011/7/6
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known th...
Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian
Twisted geometric Satake equivalence gerbes factorizable grassmannian
2011/2/28
The geometric Satake equivalence of Ginzburg and Mirkovic{ Vilonen, for a complex reductive group G, is a realization of the tensor category of representations of its Langlands dual group LG as a cat...
Quantum cohomology of the odd symplectic Grassmannian of lines
Quantum cohomology odd symplectic Grassmannian of lines
2011/2/23
Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of line...
Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Algebraic curves
Birkhoff strata the Grassmannian
2010/11/23
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rati...
Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE
Conformal geometry of surfaces Lagrangian--Grassmannian and second order PDE
2010/12/1
Of all real Lagrangian{Grassmannians LG(n; 2n), only LG(2; 4) admits a distinguished Lorentzian) conformal structure and hence is identi ed with the inde nite Mobius space S1;2.