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| Main Authors: | , |
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| Format: | Preprint |
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2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1207.3253 |
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| _version_ | 1866914657536573440 |
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| author | Gonzalez, Eduardo Woodward, Chris |
| author_facet | Gonzalez, Eduardo Woodward, Chris |
| contents | We give a quantum version of the Danilov-Jurkiewicz presentation of the cohomology of a compact toric orbifold with projective coarse moduli space. More precisely, we construct a canonical isomorphism from a formal version of the Batyrev ring to the quantum orbifold cohomology at a canonical bulk deformation. This isomorphism generalizes results of Givental, Iritani, and Fukaya-Oh-Ohta-Ono for toric manifolds and Coates-Lee-Corti-Tseng for weighted projective spaces. The proof uses a quantum version of Kirwan surjectivity and an equality of dimensions deduced using a toric minimal model program (tmmp). We show that there is a natural decomposition of the quantum cohomology where summands correspond to singularities in the tmmp, each giving rise to a collection of Hamiltonian non-displaceable tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_3253 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Quantum cohomology and toric minimal model programs Gonzalez, Eduardo Woodward, Chris Algebraic Geometry Symplectic Geometry 14N, 53D We give a quantum version of the Danilov-Jurkiewicz presentation of the cohomology of a compact toric orbifold with projective coarse moduli space. More precisely, we construct a canonical isomorphism from a formal version of the Batyrev ring to the quantum orbifold cohomology at a canonical bulk deformation. This isomorphism generalizes results of Givental, Iritani, and Fukaya-Oh-Ohta-Ono for toric manifolds and Coates-Lee-Corti-Tseng for weighted projective spaces. The proof uses a quantum version of Kirwan surjectivity and an equality of dimensions deduced using a toric minimal model program (tmmp). We show that there is a natural decomposition of the quantum cohomology where summands correspond to singularities in the tmmp, each giving rise to a collection of Hamiltonian non-displaceable tori. |
| title | Quantum cohomology and toric minimal model programs |
| topic | Algebraic Geometry Symplectic Geometry 14N, 53D |
| url | https://arxiv.org/abs/1207.3253 |