A birational Nevanlinna constant and its consequences


Min Ru

10:30:00 - 11:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will discuss some recent joint work with Paul Vojta. We introduce a modified notion, called the {\\it birational Nevanlinna constant} and denoted by $Nev_{bir}(D)$, coming from the original notation of Nevanlinna constant $Nev(D)$ introduced by Ru, for an effective divisor $D$ on a normal variety $X$. The birational Nevanlinna constant is originally defined in terms of the Weil functions, and it is proved later that it can be defined in terms of local effectivity of Cartier divisors after taking a proper birational lifting. The motivation of such modification comes from the attempting of proving a general Schmidt\'s subspace type theorem in computing Nev(D) using Autissier\'s filtration, as well as revisiting Faltings\' example in Baker\'s Garden volume from the point of view of the Nevanlinna constant. In both cases, the maximum of Weil functions must be involved, which led to the formulation of $Nev_{bir}(D)$.