Monodromy of hypergeometric functions and non-lattice integral monodromy

Monodromy of A-hypergeometric functions

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system

Monodromy at infinity of A - hypergeometric functions and toric compactifications ∗

We study A-hypergeometric functions introduced by Gelfand-KapranovZelevinsky [4] and prove a formula for the eigenvalues of their monodromy automorphisms defined by the analytic continuaions along large loops contained in complex lines parallel to the coordinate axes. The method of toric compactifications introduced in [12] and [16] will be used to prove our main theorem.

Monodromy of hypergeometric functions arising from arrangements of hyperplanes

Given an arrangement of hyperplanes in P, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of q-forms with logarithmic poles along our arrangement. We give a basis for the ideal J of relations for the Orlik-Solomon’s algebra. Under certain genericity conditions it was shown by H. Esnault, V. Schechtman and E. Viehweg that the cohomology of a local sy...

Integral Restrictions on the Monodromy

Given a complex analytic function with a one-dimensional critical locus at the origin, we examine the monodromy action on the integral cohomology of the Milnor fiber. We relate this monodromy to that of a generic hyperplane slice through the origin, and to that of a generic hyperplane slice near the origin. We thereby obtain number-theoretic restrictions on the monodromy and on the cohomology o...

Twisted L-Functions and Monodromy