Lagrangian torus fibration and mirror symmetry of Calabi-Yau hypersurface in toric variety
نویسنده
چکیده
2 Background in toric geometry 8 2.1 Basic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Toric varieties associated with a reflexive polyhedron . . . . . . . 10 2.3 Subtoric varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Singularities of a simplicial toric variety . . . . . . . . . . . . . . 12 2.5 Toric action of a torus on a toric variety . . . . . . . . . . . . . . 13 2.6 Blow up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
منابع مشابه
Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I
In this paper we start the program of constructing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric variety near the large complex limit, with respect to the restriction of a toric metric on the toric variety to the Calabi-Yau hypersurface. The construction is based on the deformation of the standard toric generalized special Lagrangian torus fibration of th...
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We consider regular Calabi-Yau hypersurfaces in N -dimensional smooth toric varieties. On such a hypersurface in the neighborhood of the large complex structure limit point we construct a fibration over a sphere S whose generic fibers are tori T. Also for certain one-parameter families of such hypersurfaces we show that the monodromy transformation is induced by a translation of the T fibration...
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1. Introduction. Strominger, Yau, and Zaslow [SYZ] conjectured that any Calabi-Yau manifold X having a mirror partner X ∨ should admit a special Lagrangian fi-bration π : X → B. (A mathematical account of their construction can be found in [M].) If so, the mirror manifold X ∨ is obtained by finding some suitable compactifi-cation of the moduli space of flat U(1)-bundles along the nonsingular fi...
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The Strominger-Yau-Zaslow conjecture proposes that mirror symmetry can be explained by the existence, in a mirror pair of Calabi-Yau manifolds, of dual special La-grangian T n-fibrations. (See [18,8,6,7] for further clarification of this conjecture.) Recently, Zharkov in [20] proved that non-singular Calabi-Yau hypersurfaces in toric varieties have topological T n-fibrations, and Ruan in [17] h...
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We describe in purely combinatorial terms dual pairs of integral affine structures on spheres which come from the conjectural metric collapse of mirror families of Calabi-Yau toric hypersurfaces. The same structures arise on the base of a special Lagrangian torus fibration in the Strominger-Yau-Zaslow conjecture. We study the topological torus fibration in the large complex structure limit and ...
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تاریخ انتشار 2008