Xinyi Yuan's Publications
The following files may be slightly different from the published versions.
My works on Arakelov geometry and algebraic dynamics:
The arithmetic Hodge index theorem for adelic line bundles II: finitely generated fields
(with Shou-Wu Zhang), preprint.
On Volumes of Arithmetic Line Bundles II, preprint.
The arithmetic Hodge index theorem for adelic
(with Shou-Wu Zhang), Math. Ann. (2016), 1-49.
Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties
(with Tong Zhang), J. Reine Angew. Math., DOI: 10.1515/crelle-2015-0025.
Relative Noether inequality on fibered surfaces
(with Tong Zhang), Adv. Math. 259 (2014), 89-115.
Volumes of Arithmetic Okounkov Bodies, Math. Z. 280 (2015), no. 3-4, 1075--1084.
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,
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), accepted by Annals of Mathematics.
- A Relative Trace Formula Proof of the Gross--Zagier Formula
(with Ye Tian and Wei Zhang), in preparation.
Triple Product L-series and Gross--Schoen Cycles
(with Shou-Wu Zhang and Wei Zhang), preprint.
Genus Periods, Genus Points and Congruent Number Problem
(with Ye Tian and Shou-Wu Zhang), to appear in Asian J. of Math.
- The Gross--Zagier Formula on Shimura Curves
(with Shou-Wu Zhang and Wei Zhang),
Annals of Mathematics Studies, Princeton University Press, 2012.
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:
Last updated: 21 Aug 2017