Back to Algebraic Geometry Seminar: Spring 2022
Algebraic Geometry Seminar
Date: Tuesday, Feb 8, 2022
Time: 3:30PM - 4:30PM
Location: See individual entries
Virtual @ 11am
Samouil Molcho
ETH Zurich
Title |
Compactifications of the Universal Jacobian via Tropical Geometry |
Abstract |
The Jacobian of the universal curve over the moduli space of stable curves is not proper. The problem of compactifying it has been the subject of long and extensive study. In parallel, an analogous theory has emerged in the realm of tropical geometry, and it has been clear that the two theories are tightly connected. In this talk, I will review the main ideas from the study of compactified Jacobians – the generalized Jacobian and stability conditions on line bundles on families of curves – and some of the tropical analogues. Then, I will discuss precisely how the two theories are connected, and how this connection allows one to translate tropical results into algebraic terms. As a consequence, I will discuss how one can obtain novel compactifications via purely tropical methods. This is based on joint work with M.Melo, M.Ulirsch, F.Viviani, J. Wise. |
Algebraic Geometry