Form–type Calabi–yau Equations
نویسندگان
چکیده
As important examples in the superstring theory and non-Kähler complex geometry, the complex manifolds #k(S 3×S3) for any k ≥ 2 [4, 11] also admit a non-vanishing holomorphic three-form [4] and a balanced metric [5]. Moreover, we know that #k(S 3 × S3) satisfies the ∂∂̄–lemma [4]. A natural question to ask is, whether #k(S 3 ×S3) admit a balanced metric ω0 such that (1.2) holds. Such a metric ω0, if exists, will play an important role in the superstring theory and hermitian geometry. More generally, let X (n ≥ 3) be a complex n-dimensional manifold with a nonvanishing holomorphic n-form Ω and with a balanced metric ω0. We want to look for a balanced metric ω such that
منابع مشابه
Mirror Symmetry of Calabi-Yau Manifolds and Flat Coordinates
We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the ordinary Picard-Fuchs equations for the periods. These equations are obtained for a class of one-parameter models and a two-parameter model of Fermat type C...
متن کاملCounting higher genus curves in a Calabi-Yau manifold
We explicitly evaluate the low energy coupling Fg in a d = 4,N = 2 compactification of the heterotic string. The holomorphic piece of this expression provides the information not encoded in the holomorphic anomaly equations, and we find that it is given by an elementary polylogarithm with index 3− 2g, thus generalizing in a natural way the known results for g = 0, 1. The heterotic model has a d...
متن کامل8 Notes on Calabi - Yau Ordinary Differential Equations ∗
We investigate the structures of Calabi-Yau differential equations and the relations to the arithmetic of the pencils of Calabi-Yau varieties behind the equations. This provides explanations of some observations and computations in the recent paper [12].
متن کاملEvaluation of Periods via Fibrations in Seiberg-Witten Theories and in Type-II String
We show how to evaluate the periods in Seiberg-Witten theories and in K3-fibered Calabi-Yau manifolds by using fibrations of the theories. In the Seiberg-Witten theories, it is shown that the dual pair of fields can be constructed from the classical fields in a simple form. As for Calabi-Yau manifolds which are fibrations of K3 surface, we obtain the solutions of the Picard-Fuchs equations from...
متن کاملGkz Hypergeometric Systems and Applications to Mirror Symmetry
Mirror symmetry of Calabi-Yau manifolds is one of the most beautiful aspects of string theory. It has been applied with great success to do non-perturbative calculation of quantum cohomology rings1−10. More recently, new ideas have been developed to apply mirror symmetry to study the moduli space of the type II string vacua compactified on a Calabi-Yau manifold. Some of the recent work on verif...
متن کاملSome Siegel threefolds with a Calabi-Yau model
2009 Introduction In the following we describe some examples of Calabi-Yau manifolds that arise as desingularizations of certain Siegel threefolds. Here by a Calabi-Yau mani-fold we understand a smooth complex projective variety which admits a holo-morphic differential form of degree three without zeros and such that the first Betti number is zero. This differential form is unique up to a const...
متن کامل