Schubert calculus and singularity theory
نویسندگان
چکیده
منابع مشابه
Cristian Lenart, Schubert Calculus Beyond K-Theory
Modern Schubert calculus has been mostly concerned with the study of the cohomology andK-theory (including their equivariant and quantum generalizations) of flag manifolds. The basic results for other cohomology theories have only been obtained recently; additional complexity is due to the dependence of the geometrically defined classes on reduced words for the corresponding Weyl group elements...
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1. Interval positroid varieties 1 1.1. Schubert varieties 1 1.2. Schubert calculus 2 1.3. First positivity result 3 1.4. Interval rank varieties 5 2. Vakil’s Littlewood-Richardson rule 7 2.1. Combinatorial shifting 7 2.2. Geometric shifting 7 2.3. Vakil’s degeneration order 9 2.4. Partial puzzles 10 3. Equivariant and Kextensions 11 3.1. K-homology 11 3.2. K-cohomology 12 3.3. Equivariant K-the...
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We describe recent work of Klyachko, Totaro, Knutson, and Tao, that characterizes eigenvalues of sums of Hermitian matrices, and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections in Grassmann varieties, and singular values of sums and products of arbitrary matrices.
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Schubert calculus refers to the calculus of enumerative geometry, which is the art of counting geometric figures determined by given incidence conditions. For example, how many lines in projective 3-space meet four given lines? This was developed in the 19th century and presented in the classic treatise ”Kälkul der abzählanden Geometrie” by Herman Cäser Hannibal Schubert in 1879. Schubert, Pier...
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The structure constants cλμ determine the classical Schubert calculus on G(m,n). It has been known for some time that the integers cλμ in formulas (1) and (2) coincide. Following the work of Giambelli [G1] [G2], this is proved formally by relating both products to the multiplication of Schur S-polynomials; a precise argument along these lines was given by Lesieur [Les]. It is natural to ask for...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2012
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2011.10.016