Collision of singular orbits for birational maps [ Back ]

Date:
18.01.16   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Anna Cima
University:
UAB

Abstract:

Birational mappings in the plane have some exceptional curves which collapse to a point. If the orbits of such a points (named singular orbits) never meet indeterminacy points of the mapping $F$, then the degree of the $n$th-iterate of $F$ is $d^n,$ where $d$ is the degree of $F$ (and the map is called algebraically stable (AS)). When one of these orbits meet an indeterminacy point of $F$, we have to perform a series of blowing-up's in order to get an AS map in an extended manifold.

In this talk I'm going to show an example in which two singular orbits have intersection. It makes the map more degenerate and multiple blow-up's are needed.