Valuations of maximal rational rank and local Weak simultaneous resolution

David Edward Fu, Purdue University

Abstract

We first study valuations of maximal rational rank, culminating in a monomialization theorem, which can be thought of as a special case of the Embedded Resolution theorem of Abhyankar and Hironaka. We then apply this theorem to extend the argument of Abhyankar in order to partially generalize his Weak local simultaneous resolution theorem for algebraic surfaces to higher dimensions in situations where the Embedded Resolution theorem holds. lastly, we make some investigations into valuations of algebraic function fields of dimension greater than or equal to three.

Degree

Ph.D.

Advisors

Abhyankar, Purdue University.

Subject Area

Mathematics

Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server
.

Share

COinS