Xinyi Yuan's Publications

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

My works on arithmetic over function fields:

Positivity of Hodge bundles of abelian varieties over some function fields, preprint, 2018.

My works on Arakelov geometry and algebraic dynamics:

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 II: finitely generated fields (with Shou-Wu Zhang), preprint.
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 description.
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.

Last updated: 21 Aug 2018