Institute of Mathematics

Modul:   MAT770  Oberseminar: Algebraische Geometrie

A wall crossing formula for degrees of real central projections (joint with Ch. Okonek)

Prof. Dr. Andrei Teleman talk

Speaker invited by: Prof. Dr. Christian Okonek

Date: 23.02.15  Time: 13.15 - 14.45  Room: Y27H25

I will discuss a recent result in real algebraic geometry: a wall crossing formula for central projections defined on submanifolds of a real projective space. This formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a $\Z$-valued degree map in a coherent way. I will discuss an interesting consequence of this result: a very general "no gap" theorem for the values of the degree map.