Vortragender: Davide Veniani, Uni Stuttgart
Titel: Towards an atlas of Enriques surfaces
One of the milestones of algebraic geometry is the classification of algebraic surfaces obtained by Castelnuovo and Enriques, revived and extended by Kodaira, Mumford and Bombieri. In this classification, Enriques surfaces played a fundamental role as the first example of non-rational surfaces with vanishing arithmetic and geometric genus. The original construction by Enriques involves a 10-dimensional family of sextic surfaces in the projective space which are non-normal along the edges of a tetrahedron.
In a joint work with G. Martin (Bonn) and G. Mezzedimi (Hannover), we study particular configurations of curves on Enriques surfaces, called (quasi-)elliptic fibrations. As a consequence of our results, we show that all Enriques surfaces arise from Enriques' original construction, as soon as the characteristic of the ground field is not 2. In this talk, I will recollect the 125-year-old history of Enriques surfaces, explain how our work fits in this story, and provide some insights into future projects.
Vortragender: Daniele Agostini, MPI Leipzig
Title: Singular curves, degenerate theta functions and KP solutions
Abstract: Smooth algebraic curves give rise to solutions to the KP equation, which models waves in shallow water, via Riemann's theta function. Singular curves produce solutions as well, but the theta function in this case becomes degenerate. I will present some results and questions in this direction, focusing on soliton and rational solutions.