Mirror symmetry and the classification of orbifold del Pezzo surfaces (Q2789850)
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scientific article; zbMATH DE number 6548665
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mirror symmetry and the classification of orbifold del Pezzo surfaces |
scientific article; zbMATH DE number 6548665 |
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Mirror symmetry and the classification of orbifold del Pezzo surfaces (English)
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2 March 2016
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orbifold Del Pezzo surfaces
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cyclic quotient singularities
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Fano polygons
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mutation-equivalence classes
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\(\mathbb Q\)-Gorenstein deformation classes
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mirror symmetry
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mutable Laurent polynomials
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This paper explores mirror symmetry for del Pezzo surfaces with cyclic quotient singularities and state a number of conjectures that together allow one to classify a broad class of such surfaces. The conjectures relate mutation-equivalence classes of Fano polygons with \(\mathbb Q\)-Gorenstein deformation classes of del Pezzo surfaces. As evidence, the authors show that their conjectures hold true in the smooth case and the case of simplest residual singularity \(\frac{1}{3}(1,1)\).
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