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"Birational Geometry and Fano varieties" dedicated to V. Iskovskikh
June 25, 2019 10:00–11:00, Moscow
 


Minimal models of surfaces with pg=1;q=0 associated with canonical Fano 3-polytopes

Victor Batyrev
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MP4 1,530.4 Mb

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Victor Batyrev
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Abstract: Let Δ be a canonical Fano 3-polytope, i.e., a 3-dimensional lattice polytope containing exactly one interior lattice point. Then the affine surface ZΔ defined by a generic Laurent polynomial fΔ with the Newton polytope Δ is birational to a smooth projective minimal surface SΔ with q=0 and pg=1. Using the classification of all 674,688 canonical Fano 3-polytopes obtained by Kasprzyk, we show that SΔ is a K3- surface except for exactly 9,089 canonical Fano 3-polytopes Δ. In the latter case, we obtain 9,040 canonical Fano 3-polytopes Δ defining minimal elliptic surfaces SΔ of Kodaira dimension 1 and 49 canonical Fano 3-polytopes Δ defining minimal surfaces SΔ of general type with |π1(SΔ)|=K2{1,2} considered by Kynev and Todorov. This is a joint work with Kasprzyk and Schaller.

Language: English
 
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