Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings
نویسندگان
چکیده
By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the corresponding coupling on the mirror model in the large complex structure limit.
منابع مشابه
The Number of Rational Quartics on Calabi-yau Hypersurfaces in Weighted Projective Space P(2, 1)
We compute the number of rational quartics on a general Calabi-Yau hypersurface in weighted projective space P(2, 1). The result agrees with the prediction made by mirror symmetry.
متن کاملMotives and Mirror Symmetry for Calabi–yau Orbifolds
We consider certain families of Calabi–Yau orbifolds and their mirror partners constructed from Fermat hypersurfaces in weighted projective 4-spaces. Our focus is the topological mirror symmetry. There are at least three known ingredients to describe the topological mirror symmetry, namely, integral vertices in reflexive polytopes, monomials in graded polynomial rings (with some group actions),...
متن کاملMotives, modularity, and mirror symmetry
We consider certain families of Calabi-Yau orbifolds and their mirror partners constructed from Fermat hypersurfaces in weighted projective spaces. We use Fermat motives to interpret the topological mirror symmetry phenomenon. These Calabi-Yau orbifolds are defined over Q, and we can discuss the modularity of the associated Galois representations. We address the modularity question at the motiv...
متن کاملMirror Symmetry and Supermanifolds
We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP becomes equivalent to a quadric in CP×CP as had been recently conjectured (in the limit where the Kähler parameter of CP, t → ±∞...
متن کاملGenus-Zero Two-Point Hyperplane Integrals in the Gromov-Witten Theory
In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point Gromov-Witten invariants of projective hypersurfaces. The integrals computed in this paper constitute a significant portion in the proof of mirror symmetry for genus-on...
متن کامل