Abstract for the talk on 27.10.2020 (17:00 h)Nonlinear Algebra Seminar Online (NASO)
Daniele Agostini (MPI MIS, Leipzig)
The birational geometry of the moduli space of curves
See the video of this talk.
The moduli space of smooth curves is one of the fundamental concepts in algebraic geometry. Severi conjectured that this space would be rational in every genus, meaning that we could write down a general Riemann surface in terms of parameters, such as the coefficients in the equation of a plane curve. This was spectacularly disproven by Harris and Mumford in the 80s and our knowledge on the birational geometry of this space has increased a lot since then. In my talk, I will present this circle of ideas, together with some recent results obtained together with Ignacio Barros.