Seminário de Geometria Algébrica e Geometria Complexa – Giusi Capobianco, (Roma 2) – 12/02 – 11h
Temos o prazer de convidar para nosso próximo Seminário de Geometria Algébrica e Geometria Complexa da UFF.
Palestrante: Giusi Capobianco, (Roma 2)
Título: A tropical version of Martens’ theorem for metric graphs
Resumo: The algebraic Martens’ theorem states that for a smooth curve C of genus g and d,r integers satisfying 0<2r\leq d<g, the dimension of the space W_d^r(C) is less or equal than d-2r and equality holds precisely when C is a hyperelliptic curve. In tropical geometry, the naive tropical analogue of this theorem has been proved by Jensen and Len not to be true. More precisely, there are non-hyperelliptic metric graphs that satisfy the equality. However, they conjectured that the theorem holds by replacing the dimension of W^r_d with a more combinatorial invariant, the so-called Brill-Noether rank. In joint work with Angelina Zheng, we study this conjecture and give a complete characterization of the hyperelliptic metric graphs. In this talk, I will first introduce divisor theory on graphs and then I will give some counterexamples to the conjecture for d=g-2+r. Finally, we will prove that for d<g-2+r, the conjecture holds.
Data: Quinta-feira, 12 de Fevereiro, 11 horas
Local: sala 407 – Bloco H – Gragoatá
Para maiores informações sobre os seminários e o histórico, basta consultar o site: https://sites.google.com/view/geoalgcompluff
