Valuations of maximal rational rank and local Weak simultaneous resolution
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
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