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Abelian variety
In
mathematics
, particularly in
algebraic geometry
,
complex analysis
and
number theory
, an
abelian variety
is a
projective algebraic variety
that is also an
algebraic group
, i.e., has a
group law
that can be defined by
regular functions
. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory.
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