Variations of Hodge Structures for Hypergeometric Differential Operators and Parabolic Higgs Bundles

Abstract

Consider the holomorphic bundle with connection on ℙ1 - {0, 1, ∞} corresponding to the regular hypergeometric differential operator (Equation Presented) If the numbers αi and βj are real and for all i and j the number αi-βj is not integer, then the bundle with connection is known to underlie a complex polarizable variation of Hodge structures. We calculate some Hodge invariants for this variation, in particular, the Hodge numbers. From this, we derive a conjecture of Alessio Corti and Vasily Golyshev. We also use non-abelian Hodge theory to interpret our theorem as a statement about parabolic Higgs bundles.