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Abelian Variety - Term Papers

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.

An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field. Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian ...

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Albanese varieties of other algebraic varieties. The group law of an abelian variety is necessarily commutative and the variety is non-singular. An elliptic curve is an abelian variety of dimension 1. Abelian varieties have Kodaira dimension ...

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"Abelian Variety." Essayworld.com. June 8, 2011. Accessed May 17, 2022. http://www.essayworld.com/essays/Abelian-Variety/99637.
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PAPER DETAILS
Added: 6/8/2011 08:00:11 PM
Submitted By: dogflicker
Category: Education
Type: Free Paper
Words: 222
Pages: 1

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