0 M ar 2 00 4 Kodaira Surface , its Extended Deformation and Mirror Image
نویسنده
چکیده
We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikov’s extended deformation theory. We provide a non-trivial example of Hertling-Manin’s weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the context of compact nilmanifolds. The calculation of extended deformation and the weak Frobenius structure is based on Merkulov’s perturbation method. The approach to relating symplectic structure and complex structure is inspired by Gualtieri’s work on generalized complex structures.
منابع مشابه
2 6 Fe b 20 04 Kodaira Surface , its Extended Deformation and Mirror Image
We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikov’s extended deformation theory. We provide a non-trivial example of Hertling-Manin’s weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the context of compact nilmanifolds. The calculation of extended deformation and ...
متن کاملExtended Deformation of Kodaira Surfaces
We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikov’s extended deformation theory. We provide a non-trivial example of Hertling-Manin’s weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image in the sense of Merkulov. The calculations of extended deformation and the weak Frobenius structure are based...
متن کاملA generalisation of the deformation variety
Given an ideal tetrahedralisation of a connected 3-manifold with nonempty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject to the gluing equations, from which one can recover a representation of the fundamental group of the manifold into the isometries of 3-dimensional hyperbo...
متن کاملType B Topological Matter , Kodaira - Spencer Theory , and Mirror Symmetry
Perturbing usual type B topological matter with vector (0, 1)-forms we find a topological theory which contains explicitly Kodaira-Spencer deformation theory. It is shown that, in genus zero, three-point correlation functions give the Yukawa couplings for a generic point in the moduli space of complex structures. This generalization of type B topological matter seems to be the correct framework...
متن کاملar X iv : a lg - g eo m / 9 30 70 02 v 1 1 4 Ju l 1 99 3 VECTOR BUNDLES AND SO ( 3 ) - INVARIANTS FOR ELLIPTIC SURFACES I
Beginning with Donaldson’s seminal paper on the failure of the h-cobordism theorem in dimension 4 [4], the techniques of gauge theory have proved to be highly successful in analyzing the smooth structure of simply connected elliptic surfaces. Recall that a simply connected elliptic surface S is specified up to deformation type by its geometric genus pg(S) and by two relatively prime integers 1 ...
متن کامل