Algebraic Geometry Seminar
Eric Riedl
University of Notre Dame
Nonfree curves and Geometric Manin's Conjecture
Abstract: Given a smooth Fano variety and a smooth curve B, let
Hom(B,X) be the moduli space of maps from B to X. Let M be a component
of Hom(B,X). If a general curve parameterized by M is free, it means M
has the expected dimension and good deformation behavior. Components M
consisting entirely of curves that are not free are more mysterious.
We give a geometric characterization of which curves can be nonfree,
explaining that roughly they come from fibrations. We show how this
result can be seen as the analogue of Manin's Conjecture, which
predicts the number of rational on a variety of bounded height. This
is joint work with Brian Lehmann and Sho Tanimoto.
Monday April 22, 2024 at 3:00 PM in 636 SEO