Colloquium Mathematics-Valente Ramirez

Title:
On fixed-point theorems and self-maps of projective spaces

Abstract:
Consider a holomorphic self-map f on the complex projective space. At
any fixed point p of f, we may look at the eigenvalues of the
derivative of f at p, which are called the multipliers of f at p. I'm
interested in understanding the collection of these numbers taken over
all the fixed points of f. In particular, I would like to understand
all the algebraic relations among these numbers.

In order to motivate the above problem I will discuss some classical
fixed-point theorems for topological spaces and for complex manifolds.
I will then explain how, in the case of self-maps of projective
spaces, these theorems constrain the possible collection of
multipliers of f. After explaining what the general problem is (which
remains quite open), I will mention some results we have in some very
particular cases.

Colloquium coordinators are Prof.dr. A.J. van der Schaft (* a.j.van.der.schaft rug.nl ) and
Dr. A.V. Kiselev (e-mail: * a.v.kiselev rug.nl )