Lectures on Monodromy

Abstract

We discuss the notions of indices of vector fields and 1-forms and their generalizations to singular varieties and varieties with actions of finite groups, as well as indices of collections of vector fields and 1-forms.

Equivariant Poincaré Series and Monodromy Zeta Functions of Quasihomogeneous Polynomials

“…Here Or X (t) is a rational function determined by the orbit types of the natural C * -action on X (see, e.g., [3]), ζ f = ζ f (t)/(1 − t) is the reduced monodromy zeta function of f , and ζ * f (t) is the Saito dual of ζ f (t) with respect to the quasidegree of the polynomial f .…”

“…The relation involved the so called Saito duality: [7], [8]. Namely, in [2], it was shown thatHere Or X (t) is a rational function determined by the orbit types of the natural C * -action on X (see, e.g., [3]), ζ f = ζ f (t)/(1 − t) is the reduced monodromy zeta function of f , and ζ * f (t) is the Saito dual of ζ f (t) with respect to the quasidegree of the polynomial f .This relation had no intrinsic explanation. It was obtained by computation of both sides and comparison of the results.…”