Algebraically motivated normal functions are algebraic. (arXiv:1810.07404v1 [math.AG])
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. As a consequence, we prove
a conjecture of Charles and Kerr-Pearlstein, that zero loci of normal functions
arising from algebraically trivial cycle classes are algebraic, and defined
over the field of definition of the family. In particular, this gives a short
proof of a special, algebraically motivated case of a result of Saito,
Brosnan-Pearlstein, and Schnell, conjectured by Green-Griffiths, on zero loci
of admissible normal functions.查看全文