Monodromy at infinity and Fourier transform

MONODROMY AT INFINITY AND FOURIER TRANSFORM II by

— For a regular twistor D-module and for a given function f , we compare the nearby cycles at f =∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf .

Monodromy at Innnity and Fourier Transform

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 zeta functions at infinity , Newton polyhedra and constructible sheaves ∗

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber [15] concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.

Monodromy at Infinity and the Weights of Cohomology

We show that the size of the Jordan blocks with eigenvalue one of the monodromy at infinity is estimated in terms of the weights of the cohomology of the total space and a general fiber. Let f : X → S be a morphism of complex algebraic varieties with relative dimension n. Assume S is a smooth curve. Let U be a dense open subvariety of S such that the H(Xs,Q) for s ∈ U form a local system (which...