Fields of moduli and fields of definition of odd signature curves

Details Fields of moduli and fields of definition of odd signature curves Fields of moduli and fields of definition of odd signature curves

2011-11-18

arxiv.org/abs/1111.4489v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

Let $X$ be a smooth projective algebraic curve of genus $g\geq 2$ defined over a field $K$. We show that $X$ can be defined over its field of moduli if it has odd signature, i.e. if the signature of the covering $X\to X/\Aut(X)$ is of type $(0;c_1,...,c_k)$, where some $c_i$ appears an odd number of times. This result is applied to $q$-gonal curves and to plane quartics. For $q$-gonal curves, we prove that non-normal $q$-gonal curves can be defined over their field of moduli and we construct examples of normal $q$-gonal curves with field of moduli $\mathbb{R}$ that can not be defined over $\mathbb{R}$. For plane quartics, we prove that they can be defined over their field of moduli if the automorphism group is not isomorphic to either $C_2$ or $C_2\times C_2$.

Affiliated with

Also associated with

No associations

Rating

Fields of moduli and fields of definition of odd signature curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fields of moduli and fields of definition of odd signature curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fields of moduli and fields of definition of odd signature curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-514194