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arXiv · 0804.0578

Characteristic polynomials of automorphisms of hyperelliptic curves

Robert M. Guralnick·Everett W. Howe
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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.

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Robert M. Guralnick, Everett W. Howe. 2008-04-03. Characteristic polynomials of automorphisms of hyperelliptic curves. https://arxiv.org/abs/0804.0578

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