LAGRANGIAN FIBRATIONS ON BLOWUPS OF TORIC VARIETIES AND MIRROR SYMMETRY FOR HYPERSURFACES

被引：46

作者：

Abouzaid, Mohammed ^{[1
]}

Auroux, Denis ^{[2
]}

Katzarkov, Ludmil ^{[3
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] Univ Vienna, Fak Math, Waehringer Guertel 18, A-1090 Vienna, Austria

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2016年 / 123卷 / 01期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

FLOER COHOMOLOGY; TORUS FIBERS; MANIFOLDS; PAIRS;

D O I：

10.1007/s10240-016-0081-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface in a toric variety we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of along , under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a Landau-Ginzburg model which can be naturally viewed as a mirror to . The main applications concern affine hypersurfaces of general type, for which our results provide a geometric basis for various mirror symmetry statements that appear in the recent literature. We also obtain analogous results for complete intersections.

引用

页码：199 / 282

页数：84