Julie Wang: On Campana's conjecture for covering of toric varieties
Abstract: In joint work with Guo, Nguyen, and Sun, we extend results of Corvaja–Zannier, Turchet and Capuano-Turchet to establish cases of the Lang-Vojta Conjecture for varieties of log general type that arise as ramified covers of algebraic tori over function fields. The central technical result involves proving a version of Vojta’s generalized abc conjecture for algebraic tori over function fields, with explicitly computable exceptional sets. This is achieved through a GCD theorem for multivariable polynomials evaluated at S-unit arguments.
In this talk, I will discuss how these results can be further extended to derive Campana’s orbifold conjecture for toric varieties with high multiplicities along the boundary, both over function fields and for entire curves. This part of the work is in collaboration with Carlo Gasbarri and Ji Guo in the function field case and with Min Ru in the complex analytic setting.
Carlo Gasbarri: Rational points on expanding domains
Abstract: If X is a projective variety defined over a number field and M is a complex relatively compact Riemann surface contained in it, Bombieri and Pila estimate the number of rational points contained in M in terms of their height. In this talk we will present some similar estimate when we consider the set of rational points in the image of a Zariski dense holomorphic map from the complex plane in a variety.
I seminari si svolgeranno in presenza presso il Dipartimento di Matematica e Fisica, via della Vasca Navale 84 - aula B.
Per ulteriori informazioni, si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.
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