Weak Landau-Ginzburg models for smooth Fano threefolds

被引:24
作者
Przyjalkowski, V. V. [1 ]
机构
[1] RAS, Steklov Math Inst, Moscow, Russia
关键词
weak Landau-Ginzburg models; Fano varieties; toric degeneration; intermediate Jacobian; MIRROR SYMMETRY; COMPLETE-INTERSECTIONS; TORIC DEGENERATIONS; SURFACES;
D O I
10.1070/IM2013v077n04ABEH002660
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider Landau-Ginzburg models for smooth Fano threefolds of the principal series and prove that they can be represented by Laurent polynomials. We check that these models can be compactified to open Calabi-Yau varieties. In the spirit of Katzarkov's programme we prove that the numbers of irreducible components of the central fibres of compactifications of these pencils are equal to the dimensions of intermediate Jacobians of the corresponding Fano varieties plus 1. In particular, these numbers are independent of the choice of compactification. We state most of the known methods for finding Landau-Ginzburg models in terms of Laurent polynomials. We discuss the Laurent polynomial representation of the Landau-Ginzburg models of Fano varieties and state some related problems.
引用
收藏
页码:772 / 794
页数:23
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