280 citations · 1.6k across the 92 of their papers we have counts for
11 papers · 1 filter
Real Regulators for Products of Elliptic Curves
Xi Chen, James D. Lewis
Assuming the Kunneth decomposition of the Chow groups of products of general Kummer surfaces, we prove that the Hodge--conjecture fails for the real regulator $r_{k,1…
Algebraic Hyperbolicity of Complements of Generic Hypersurfaces in Projective Spaces
Xi Chen, Eric Riedl, Wern Yeong
We study the algebraic hyperbolicity of the complement of very general degree hypersurfaces in P^n. We prove the Algebraic Green-Griffiths-Lang Conjecture for these complement…
Automorphism and Cohomology II: Complete intersections
Xi Chen, Xuanyu Pan, Dingxin Zhang
We prove that the automorphism group of a general complete intersection in a projective space is trivial with a few well-understood exceptions. We also prove that the automorph…
Dynamics of Special Points on Intermediate Jacobians
Xi Chen, James D. Lewis
We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic…
Real Regulators on Self-Products of K3 Surfaces
Xi Chen, James D. Lewis
Based on a novel application of an archimedean type pairing to the geometry and deformation theory of surfaces, we construct a regulator indecomposable -class on a self-p…
On Vojta's Conjecture
Xi Chen
I gave a geometric proof of Vojta's 1 + epsilon conjecture. Some gaps in the published paper were spotted and kindly pointed out to me by Paul Vojta. These were addressed in "Errat…