Seminario di Geometria

Giovedì 14 Marzo alle ore 14:15, Francesco Ballini (University of Oxford) terrà il seminario di Geometria dal titolo "Unlikely Double Intersections".

Abstract: The Zilber-Pink Conjecture, which should rule the behaviour of intersections between an algebraic variety and a countable family of "special varieties", does not take into account double intersections; some results related to tangencies with special subvarieties have been obatined by Marché-Maurin in 2014 in the case of the square of the multiplicative group and by Corvaja-Demeio-Masser-Zannier in 2019 in the case of elliptic schemes. We prove that any algebraic curve contained in Y(1)^2 is tangent to finitely many modular curves (which are the one-codimensional special subvarieties) and, together with Capuano, we generalize the result of Marché-Maurin to arbitrary powers of the multiplicative group. No previous knowledge of the topic is required: we will explain the general Zilber-Pink Conjecture philosophy, we will describe the main tools used in this context and we will see what are the differences in the double intersection case.

Il seminario si svolgerà in presenza nell'aula M1. Per ulteriori informazioni, si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.