Xinyi Yuan's Publications

The following files may be slightly different from the published versions.

My recent works:

Partial heights, entire curves, and the geometric Bombieri-Lang conjecture (with Junyi Xie), 2023.
The geometric Bombieri-Lang conjecture for ramified covers of abelian varieties (with Junyi Xie), 2023.
Modular heights of quaternionic Shimura curves, 2022.
Explicit Kodaira-Spencer map over Shimura curves, 2022.
Arithmetic bigness and a uniform Bogomolov-type result, 2021.
Adelic line bundles over quasi-projective varieties (with Shou-Wu Zhang), 2021.
The arithmetic Hodge index theorem for adelic line bundles II: finitely generated fields (with Shou-Wu Zhang), 2021.

My works on Arakelov geometry, arithmetic geometry and algebraic dynamics:

Geometric Bogomolov conjecture in arbitrary characteristics (with Junyi Xie), Invent. Math. 229 (2022), no.2, 607-637.
Positivity of Hodge bundles of abelian varieties over some function fields, Compos. Math. 157 (2021), no. 9, 1964-2000.
Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties (with Tong Zhang), J. Reine Angew. Math. 736 (2018), 255-284.
The arithmetic Hodge index theorem for adelic line bundles (with Shou-Wu Zhang), Math. Ann. 367 (2017), no. 3-4, 1123-1171.
Volumes of Arithmetic Okounkov Bodies, Math. Z. 280 (2015), no. 3-4, 1075--1084.
Relative Noether inequality on fibered surfaces (with Tong Zhang), Adv. Math. 259 (2014), 89-115.
Effective Bound of Linear Series on Arithmetic Surfaces (with Tong Zhang), Duke Math. J. 162 (2013), no. 10, 1723-1770.
On Volumes of Arithmetic Line Bundles II, preprint, 2009.
On Volumes of Arithmetic Line Bundles, Compositio Mathematicae 145 (2009), 1447-1464.
Big Line Bundles over Arithmetic Varieties, Inventiones Mathematicae 173 (2008), no. 3, 603--649.

My works on automorphic forms, Shimura varieties and L-functions:

On the averaged Colmez conjecture (with Shou-Wu Zhang), Ann. of Math. (2) 187 (2018), no. 2, 533-638.
Genus Periods, Genus Points and Congruent Number Problem (with Ye Tian and Shou-Wu Zhang), Asian J. Math. 21 (2017), no. 4, 721-773.
A Relative Trace Formula Proof of the Gross--Zagier Formula (with Ye Tian and Wei Zhang), in preparation.
The Gross--Zagier Formula on Shimura Curves (with Shou-Wu Zhang and Wei Zhang), Annals of Mathematics Studies, Princeton University Press, 2012. Please see the erratum.
Triple Product L-series and Gross--Schoen Cycles (with Shou-Wu Zhang and Wei Zhang), preprint, 2010.
The Gross--Kohnen--Zagier Theorem over Totally Real Fields (with Shou-Wu Zhang and Wei Zhang), Compositio Mathematicae 145 (2009), 1147-1162.

My expository works:

Algebraic Dynamics, Canonical Heights and Arakelov Geometry, Fifth International Congress of Chinese Mathematicians. Part 1, 2, 893-929, Amer. Math. Soc., Providence, RI, 2012.
On Faltings heights of abelian varieties with complex multiplication, Proceedings of the Seventh International Congress of Chinese Mathematicians, Vol. I, 521-536, Adv. Lect. Math. (ALM), 43, Int. Press, Somerville, MA, 2019.

Last updated: August 2023