Characteristic polynomials of automorphisms of hyperelliptic curves
نویسنده
چکیده
Let α be an automorphism of a hyperelliptic curve C of genus g and let α be the automorphism induced by α on the genus-0 quotient of C by the hyperelliptic involution. Let n be the order of α and let n be the order of α. We show that the characteristic polynomial f of the automorphism α∗ of the Jacobian of C is determined by the values of n, n, and g, unless n = n, n is even, and (2g + 2)/n is even, in which case there are two possibilities for f . In every case we give explicit formulas for the possible characteristic polynomials.
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