80 citations · 162 across the 21 of their papers we have counts for
6 papers · 1 filter
Geometric Bogomolov conjecture in arbitrary characteristics
Junyi Xie, Xinyi Yuan
The goal of this paper is to prove the full geometric Bogomolov conjecture. We first reduce it to the case that the extension of the base fields has transcendence degree 1, and the…
Comparison of arithmetic Brauer groups with geometric Brauer groups
Xinyi Yuan
Let be a projective and smooth variety over a field . The goal of this paper is to prove that the cokernel of the canonical map has a finite exp…
Positivity of Hodge bundles of abelian varieties over some function fields
Xinyi Yuan
The main result of this paper concerns the positivity of the Hodge bundles of abelian varieties over global function fields. As applications, we obtain some partial results on the…
Relative Noether inequality on fibered surfaces
Xinyi Yuan, Tong Zhang
We prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic. It can be viewed as a…
On Volumes of Arithmetic Line Bundles II
Xinyi Yuan
For a hermitian line bundle over an arithmetic variety, we construct a convex continuous function on the Okounkov body associated to the generic fibre of the line bundle. The integ…
On Volumes of Arithmetic Line Bundles
Xinyi Yuan
We show an arithmetic generalization of the recent work of Lazarsfeld-Mustata which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-co…