Gluing and ungluing curves of low genus

Wednesday, November 14, 2018
Ora Inizio: 
Ora Fine: 
Davide Lombardo
Università di Pisa

From the problem of determining the endomorphism algebra of an abelian variety – typically a Jacobian – one is naturally led to consider an operation of gluing between curves of low genus: given curves C1, C2 of genera g1, g2 respectively, if g1+g2 < 4 there are countably many ways to glue C1 and C2 to get a new curve C of genus g1+g2. This gluing operation is easy to describe at the level of the Jacobians of C1, C2 and C, but it would be interesting to reformulate it purely in terms of the geometry of the curves. This should be particularly relevant to the problem of ungluing, namely, the question of recovering C1 and C2 from C. I'll describe some of the characters relevant to this problem - polarisations on abelian varieties, Prym varieties, the Chevalley-Weil formula - and present a family of genus 3 curves (obtained by 3-gluing) for which the ungluing problem can be solved in purely geometric terms.

Questo è un seminario espositivo, indirizzato anche a studenti di dottorato e della magistrale.