Realisation of birational maps

par Anna Bot (University of Basel)

jeudi 17 nov. 2022, 10:30 → 11:30 Europe/Paris

salle 207 bâtiment 1R2 (Institut de Mathématiques de Toulouse)

Given a matrix F in GL_n(ℤ), we investigate under which conditions it can be 

realized as a birational map f of ℙ², meaning if there exists a blow-up to a 

rational surface X on which f lifts to an automorphism whose action on the Picard 

group of X is precisely F. Based on ideas by McMullen and Uehara, we give 

sufficient conditions on points on a cuspidal cubic, and indicate how this can 

be used to prove that the ordinal of all dynamical degrees of all birational maps 

of ℙ² is ω^ω.