Coble surfaces and Desargues configurations of lines and points
- Igor Dolgachev (University of Michigan)
A beautiful theorem of J. Thas asserts that the ten points of a Desargues configuration of lines and points formed by two perspective triangles in the projective plane can serve as the ten nodes of a unique rational plane curve of degree 6. I will give an algebraic-geometric proof of this theorem by using the geometry of a special Coble surfaces obtained as blow-ups of ten nodes of a rational sextic. We will also discuss an interesting dynamics of automorphisms of these special Coble surfaces.