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Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons

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arxiv 1810.07404 v2 pith:5ZCO35BD submitted 2018-10-17 math.AG

Jeff Achter , Sebastian Casalaina-Martin , Charles Vial This is my paper · ORCID
classification math.AG
keywords algebraicfunctionsalgebraicallydefineddefinitionfieldnormaltrivial
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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.

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  1. Cycle class maps and birational invariants

    math.AG 2019-08 conditional novelty 7.0 of 10

    A new invariant from cycle maps on curves shows that a smooth threefold intersection of two quadrics over a subfield of C is rational if and only if it contains a line over that field.

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