Gary Kennedy : Monodromy of quasi-ordinary singularities

Posted by , part of the Algebraic Geometry Seminar.

At

Feb. 28, 2008, 4 p.m.

In

SEO 636

Abstract

A quasi-ordinary surface f(x,y)=0 is one for which, at each singular point, there is a theory of Puiseux expansion as for plane curves. Taking a transverse slice with x=constant, one obtains a singular plane curve. Its Milnor fiber f(x,y)=e has two sorts of monodromy: (1) the Milnor monodromy (also called its horizontal monodromy), in which x is fixed while e varies around a small circle, (2) the vertical monodromy, in which e is fixed while x varies. In joint work with my colleague Lee McEwan, we have discovered simple recursive formulas for both monodromies.