Quantum Sheaf Cohomology on Grassmannians
نویسندگان
چکیده
منابع مشابه
Quantum cohomology of Grassmannians
The (small) quantum cohomology ring of a Grassmann variety encodes the enumerative geometry of rational curves in this variety. By using degeneracy loci formulas on quot schemes, Bertram has proved quantum Pieri and Giambelli formulas which give a complete description of the quantum cohomology ring. In this talk I will present elementary new proofs of these results which rely only on the defini...
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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 cohomology ring QH∗(OG) and show that its product structure is determined by the ring of P̃ -polynomials. A ‘quantum Schubert calculus’ is formulated, which includes quantum Pieri and Giambelli formu...
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We discuss a new approach to the quantum cohomology ring of a Grassmannian. This ring is also isomorphic to the Verlinde algebra. We present a formula for the quantum product of Schubert classes (3-point GromovWitten invarints), or, equivalently, for the fusion product in sl(k). The main combinatorial tool is a cylindric analogue of Young tableux. The formula immediately implies several new ide...
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The goal of this note is to give an example for which Theorem 1.1 fails if we only relax the hypothesis that X is quasi-compact (Propositions 2.3 and 3.1). This example emerged from the author’s investigation on local cohomology of valuation rings [Dat16]. In particular, some results from [Dat16, Sections 6, 7] are reproduced below without citation. Any other outside result we use is accompanie...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2016
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-016-2763-z