Article

# On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau Threefolds

Journal of Geometric Analysis (Impact Factor: 0.86). 06/2005; DOI: 10.1007/BF02930760

Source: arXiv

- [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we first study the moduli spaces related to Calabi-Yau manifolds. We then apply the results to the following problem. Let C be a fixed Riemann surface with fixed finite number of points on it. Given a CY manifold with fixed topological type, we consider the set of all families of CY manifolds of the fixed topological type over C with degenerate fibres over the fixed points up to isomorphism. This set is called Shafarevich set. The analogue of Shafarevich conjecture for CY manifolds is for which topological types of CY the Shafarevich set is finite. It is well-known �This work is partially supported by the Institute of Mathematical Sciences, CUHK - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we prove a Gauss–Bonnet–Chern type theorem in full generality for the Chern–Weil forms of Hodge bundles. That is, the Chern–Weil forms compute the corresponding Chern classes. This settles a long standing problem. Second, we apply the result to Calabi–Yau moduli, and proved the corresponding Gauss–Bonnet–Chern type theorem in the setting of Weil–Petersson geometry. As an application of our results in string theory, we prove that the number of flux vacua of type II string compactified on a Calabi–Yau manifold is finite, and their number is bounded by an intrinsic geometric quantity.Mathematische Annalen 10/2013; · 1.38 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This is the first of series of articles in which we are going to study the regularized determinants of the Laplacians of Calabi Yau metrics acting on (0,q) forms on the moduli space of CY manifolds with a fixed polarization. It is well known that in the case of elliptic curves, the Kronecker limit formula gives an explicit formula for the regularized determinant of the flat metric with fixed volume on the elliptic curves. The following formula holds in this case

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.