6 papers
Motivic integration on Berkovich spaces
Tommaso de Fernex, Chung Ching Lau
We define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The c…
Extending rationally connected fibrations from ample subvarieties
Tommaso de Fernex, Chung Ching Lau
Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly sin…
Grothendieck--Lefschetz for ample subvarieties
Tommaso de Fernex, Chung Ching Lau
We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more gene…
The gonality of complete intersection curves
James Hotchkiss, Chung Ching Lau, Brooke Ullery
The purpose of this paper is to show that for a complete intersection curve in projective space (other than a few stated exceptions), any morphism satis…
Numerical dimension and locally ample curves
Chung-Ching Lau
In the paper \cite{Lau16}, it was shown that the restriction of a pseudoeffective divisor to a subvariety with nef normal bundle is pseudoeffective. Assuming the normal bun…
On nef subvarieties
Chung-Ching Lau
The goal of this work is to study positivity of subvarieties with nef normal bundle in the sense of intersection theory. After Ottem's work on ample subschemes, we introduce the no…