Explicit galois obstruction and descent for
hyperelliptic curves with tamely cyclic reduced automorphism group.
Mathematics of Computation, January 2015.
This paper is devoted to the study of the Galois descent
obstruction for hyperelliptic curves of arbitrary genus
whose reduced automorphism groups are cyclic of order
coprime to the characteristic of their ground field. We give
an explicit and effectively computable description of this
obstruction. Along the way, we obtain an arithmetic
criterion for the existence of a so-called hyperelliptic
We define homogeneous dihedral invariants for
general hyperelliptic curves, and show how the obstruction
can be expressed in terms of these invariants. If this
obstruction vanishes, then the homogeneous dihedral
invariants can also be used to explicitly construct a model
over the field of moduli of the curve; if not, then one
still obtains a hyperelliptic model over a degree 2
extension of the field of moduli.
[ bib |