About the equivalence of divisor classes on hyperelliptic curves and a quotient of linear forms by an algebraic group action

Details About the equivalence of divisor classes on hyperelliptic curves and a quotient of linear forms by an algebraic group action About the equivalence of divisor classes on hyperelliptic curves and a quotient of linear forms by an algebraic group action

2006-04-26

arxiv.org/abs/math/0604545v1

Mathematics

Algebraic Geometry

Scientific paper

For a hyperelliptic curve of genus $g$, a divisor in general position of
degree $g+1$ is given by polynomial equations. There is an action from an
algebraic group on the representations of divisors by polynomials which fixes
divisor classes. This structure reduces the question of rationality of divisor
classes to rationality of polynomials which is more easy to control.

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