On the canonical ring of algebraic varieties
In this paper we study the curvature tensor of the Riemannian metric defined in a natural way on the moduli space of compact special Lagrangian submanifolds of a Calabi-Yau manifold. We state some curvature properties and we prove that the Ricci curvature is non negative under an assumption on the determinant of .
We study threefolds having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many embeddings...