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Modul:   MAT770  Oberseminar: Algebraische Geometrie


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

Prof. Dr. Andrei Teleman's talk

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.