Alan Durfee

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alg-geom1997

Five Definitions of Critical Point at Infinity

Alan H. Durfee

This survey paper discusses five equivalent ways of defining a ``critical point at infinity'' for a complex polynomial of two variables.

alg-geom1995

The index of $g r a df (x, y)$

Alan H. Durfee

Let $f (x, y)$ be a real polynomial of degree $d$ with isolated critical points, and let $i$ be the index of $g r a df$ around a large circle containing the critical points. An element…

alg-geom1993

Intersection homology Betti numbers

Alan H. Durfee

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of in…

Five Definitions of Critical Point at Infinity

The index of gradf(x,y)

Intersection homology Betti numbers

The index of $g r a df (x, y)$