Characteristic polynomials of automorphisms of hyperelliptic curves
Algebraic Geometry
2010-01-23 v1
Abstract
Let alpha be an automorphism of a hyperelliptic curve C of genus g, and let alpha' be the automorphism of P^1 induced by alpha. Let n be the order of alpha and let n' be the order of alpha'. We show that the triple (g,n,n') completely determines the characteristic polynomial of the automorphism alpha^* of the Jacobian of C, unless n is even, n=n', and (2g+2)/n is even, in which case there are two possibilities. We give explicit formulas for the characteristic polynomial in all cases.
Cite
@article{arxiv.0804.0578,
title = {Characteristic polynomials of automorphisms of hyperelliptic curves},
author = {Robert M. Guralnick and Everett W. Howe},
journal= {arXiv preprint arXiv:0804.0578},
year = {2010}
}
Comments
LaTeX, 11 pages