On a canonical class of Green currents for the unit sections of abelian schemes

Details On a canonical class of Green currents for the unit sections of abelian schemes On a canonical class of Green currents for the unit sections of abelian schemes

2011-07-27

arxiv.org/abs/1107.5600v1

Mathematics

Algebraic Geometry

38 pages

Scientific paper

We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar\partial$-exact differential forms. This current generalizes the Siegel functions defined on elliptic curves. We prove generalizations of classical properties of Siegel functions, like distribution relations, limit formulae and reciprocity laws.

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