Shafarevich’s Conjecture for CY Manifolds I (Moduli of CY Manifolds)
نویسندگان
چکیده
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 that the analogue of Shafarevich conjecture is closely related to the study of the moduli space of polarized CY manifolds and the moduli space of the maps of fixed Riemann surface to the coarse moduli space of the
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