Mirror symmetry for log Calabi-Yau surfaces I
| Autor: | Gross, Mark, Hacking, Paul, Keel, Sean |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give a canonical synthetic construction of the mirror family to a pair (Y,D) of a smooth projective surface with an anti-canonical cycle of rational curves, as the spectrum of an explicit algebra defined in terms of counts of rational curves on Y meeting D in a single point. In the case D is contractible, the family gives a smoothing of the dual cusp, and thus a proof of Looijenga's 1981 cusp conjecture. Comment: 144 pages, 3 figures, Second version significantly shorter, 109 pages. The first version has a lot of material (particularly in the introduction and material on cyclic quotient singularities) which does not appear in the new version. Download version 1 if this material is desired. Third and final version, small changes from Version 2, to appear in Publ. IHES |
| Databáze: | arXiv |
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