Small points on rational subvarieties of tori

Compactifications of Subvarieties of Tori

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary divisors intersect in codimension k. We consider some examples including M0,n ⊂ M0,n (and more generally log canonical models of complements of hyperplane arrangem...

Pluriharmonic Tori, Configurations of Points on Rational or Elliptic Curves and Another Type of Spectral Data

This paper is made up of five sections. The first four sections are expositary notes of [9] and [10]. In the last section, we introduce another type of spectral data. Recently, McIntosh [5] proved that some class of pluriharmonic maps from complex vector spaces into complex Grassmann manifolds or projective unitary groups correspond to maps constructed from triplets (X,π,L), consisting of auxil...

Distribution of Rational Points: A Survey

Integral Points on Subvarieties of Semiabelian Varieties, Ii

This paper proves a finiteness result for families of integral points on a semiabelian variety minus a divisor, generalizing the corresponding result of Faltings for abelian varieties. Combined with the main theorem of the first part of this paper, this gives a finiteness statement for integral points on a closed subvariety of a semiabelian variety, minus a divisor. In addition, the last two se...

Rational Points on Quartics