Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes
نویسندگان
چکیده
منابع مشابه
Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian
Let LGn denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension 2n. For each strict partition λ = (λ1, . . . , λk) with λ1 ≤ n there is a Schubert variety X(λ). Let T denote a maximal torus of the symplectic group acting on LGn. Consider the T -equivariant cohomology of LGn and the T -equivariant fundamental class...
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We give positive formulas for the restriction of a Schubert Class to a T -fixed point in the equivariant K-theory and equivariant cohomology of the Grassmannian. Our formulas rely on a result of Kodiyalam-Raghavan and Kreiman-Lakshmibai, which gives an equivariant Gröbner degeneration of a Schubert variety in the neighborhood of a T -fixed point of the Grassmannian.
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The product of two Schubert cohomology classes on a Grassmannian Grk(C) has long been known to be a positive combination of other Schubert classes, and many manifestly positive formulae are now available for computing such a product (e.g., the Littlewood-Richardson rule or the more symmetric puzzle rule from A. Knutson, T. Tao, and C. Woodward [KTW]). Recently, W. Graham showed in [G], nonconst...
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Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still relatively poorly understood. We discuss here the weighted projective analogs of homogeneous spaces such as the Grassmannian Gr(2, 5) and ort...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnu003