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

被引：49
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：
奥地利科学基金会; 美国国家科学基金会;
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.
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页码：199 / 282
页数：84
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