Infinitestimal Variation of Hodge Structures and the Weak Global Torelli Theorem for Complete Intersections

Abstract

In this paper, we will study the weak global Torelli theorem for complete intersections of hypersurfaces in a projective space. Let X be a non-singular projective variety of dimension r with an ample line bundle L over the complex number field C. Then the primitive part Hrm(X, Z) of the cohomology of X has a polarized Hodge structure. If the moduli space X of X exists, we can define the global period map Ho-* D/r from the moduli space X to the classifying space D/r of Hodge structures attaching the point p in X to the Hodge structure of the primitive part Hrim(Xp, Z) of the cohomology group of Xp(p E 4').