Bounding the genus of subvarieties of generic hypersurfaces from below

Abstract

A second-order invariant of C. Voisin gives a powerful method for bounding from below the geometric genus of a k-dimensional subvariety of a degree-d hypersurface in complex projective n-space. This work uses the Voisin method to establish a general bound, which lies behind recent results of G. Pacienza and Z. Ran.