Dipartimento di Matematica, Università Roma Tre
Julie Wang (Academia Sinica)
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 in the function field case and with Min Ru in the complex analytic setting.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
amos.turchet@uniroma3.it