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QUANTUM COHOMOLOGY OF ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS QUANTUM COHOMOLOGY
2015/12/17
Let V be a vector space with a nondegenerate symmetric form and
OG be the orthogonal Grassmannian which parametrizes maximal isotropic
subspaces in V . We give a presentation for the (small) quantum...
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum
cohomology ring of G=P. We also give a presentation of this ring i...
Let G be a semisimple complex algebraic group and P a parabolic subgroup of G.
The homogeneous space X = G=P is a projective complex manifold. My aim in
this lecture is to survey what is known about...
It is well known that the real cohomology of a compact Riemannian manifold
M is isomorphic to the algebra of its harmonic forms. When M is a fiat
Riemannian manifold, i.e. a Euclidean manifold, a ...
Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus
homogeneous spaces generalized Schubert calculus
2015/7/14
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We
give various ext...
Hodge cohomology of iterated fibred cusp metrics on Witt spaces
Hodge cohomology iterated fibred cusp metrics Witt spaces Differential Geometry
2012/6/21
On a Witt space, we identify the $L^2$ cohomology of iterated fibred cusp metrics with the middle perversity intersection cohomology of the corresponding stratified space.
Techniques of computations of Dolbeault cohomology of solvmanifolds
Dolbeault cohomology solvmanifolds Differential Geometry
2011/9/20
Abstract: We consider semi-direct products $\C^{n}\ltimes_{\phi}N$ of Lie groups with lattices $\Gamma$ such that $N$ are nilpotent Lie groups with left-invariant complex structures. We compute the Do...
On tangential cohomology attached to a function on complex foliations
complex foliations cohomology
2011/1/18
In this note we study a new cohomology attached to a function along the leaves of complex foliations. We also explain how this cohomology depends on the function and we study a relative cohomology and...
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
Cohomology Toric Varieties Local Monomial Supports
2010/11/1
We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each com...