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BIMSA Lecture
BIMSA Lecture
Deautonomisation by singularity confinement and degree growth of birational maps of the plane
Deautonomisation by singularity confinement and degree growth of birational maps of the plane
Organizer
Speaker
Alexander Stokes
Time
Tuesday, April 14, 2026 3:30 PM - 4:30 PM
Venue
A6-101
Online
Zoom 537 192 5549
(BIMSA)
Abstract
For a discrete dynamical system defined by a birational mapping of the plane, growth of complexity is measured by its algebraic entropy. In the field of discrete integrable systems there is a procedure called deautonomisation by singularity confinement, that produces a non-autonomous version of the system, i.e. a sequence or family of maps, with the same structure of singularities. In studying examples, the surprising observation was made that the algebraic entropy is reflected in the conditions required of evolution of the parameters in the map when deautonomised. In this talk we sketch a geometric explanation of this phenomenon, using a kind of period map for rational surfaces with effective anticanonical divisor.