Seminars & Colloquia Calendar
Curves, maps, and singularities in genus one
Dhruv Ranganathan -- MIT
Location: Hill 425
Date & time: Wednesday, 21 February 2018 at 2:00PM - 3:00PM
Abstract: I will outline a new framework based on tropical and logarithmic methods to study genus one curve singularities and discuss its relationship with the geometry of moduli spaces. I will focus on two applications of these ideas.
First, they allow one to explicitly factorize the rational maps among log canonical models of the moduli space of n-pointed elliptic curves. Second, they reveal a modular interpretation for Vakil and Zinger's famous desingularization of the space of elliptic curves in projective space, a short conceptual proof of that result, and several new generalizations.
Time permitting, though it rarely does, I will mention some applications to both classical and virtual enumerative geometry.
This is based on work with Len and with Santos-Parker and Wise, as well as ongoing work with Battistella and Nabijou.