NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS

For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of def...

Full description

Saved in:
Bibliographic Details
Published in:Forum of mathematics. Sigma 2019, Vol.7, Article e36
Main Authors: ACHTER, JEFFREY D., CASALAINA-MARTIN, SEBASTIAN, VIAL, CHARLES
Format: Article
Language:English
Subjects:
14C25
14C30
14D07
14D10
14G99
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For families of smooth complex projective varieties, we show that normal functions arising from algebraically trivial cycle classes are algebraic and defined over the field of definition of the family. In particular, the zero loci of those functions are algebraic and defined over such a field of definition. This proves a conjecture of Charles.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2019.34