5 papers
Equidistribution for quasi-projective varieties over function fields
Debam Biswas, Yulin Cai
We prove equidistribution of small points and subvarieties on quasi-projective varieties over function fields, confirming \cite[Conjecture~5.4.1]{yuan2021adelic} for compactified r…
Concave transforms of compactified S-metrized divisors
Debam Biswas, Yulin Cai
We associate a concave transform to any compactified S-metrized divisor on a quasi-projective variety over an adelic curve. Then we show a Hilbert-Samuel type formula for relativel…
Differentiability of Adelic Volumes and Equidistribution on Quasi-Projective Varieties
Debam Biswas
Differentiability of geometric and arithmetic volumes of Hermitian line-bundles leads to the proof of equidistribution results on projective varieties using the variational princip…
Convex Bodies associated to Linear series of Adelic Divisors on Quasi-Projective Varieties
Debam Biswas
In this article we define and study convex bodies associated to linear series of adelic divisors over quasi-projective varieties that have been introduced recently by Xinyi Yuan an…
A dynamical version of Silverman-Tate's height inequality
Debam Biswas, Zhelun Chen
In the paper "Uniformity of Mordell-Lang" by Vesselin Dimitrov, Philipp Habegger and Ziyang Gao (arXiv:2001.10276), they use Silverman-Tate's Height Inequality and they give a proo…