Subgroups of PGL2 and birational automorphisms of algebraic surfaces

Seminar: 
Algebraic and Tropical Geometry
Event time: 
Friday, March 2, 2018 - 4:00pm to 5:00pm
Speaker: 
Daniel Allcock
Speaker affiliation: 
University of Texas
Event description: 

Arthur Coble constructed a family of rational surfaces with a smooth rational curve invariant under every surface automorphism (the curve isbi-anticanonical), with a very large group of symmetries(a lattice in SO(9,1)). Coble conjectured that generically thisgroup is faithful on the rational curve, which would be quiteinterestingeven from a purely lattices-in-Lie-groups perspective.We will discuss some related ideas, including a particular surface for which the symmetry group can be worked outexactly\; while it is far from discrete in PGL2(C), it turns out tobe a lattice in PGL2(Q3). (Joint work with Igor Dolgachev.)