Hyperelliptic curves over F_2 of every 2-rank without extra automorphisms

Details Hyperelliptic curves over F_2 of every 2-rank without extra automorphisms Hyperelliptic curves over F_2 of every 2-rank without extra automorphisms

2006-08-07

arxiv.org/abs/math/0608156v1

Proc. Amer. Math. Soc. 134 (2006), no. 2, 323--331

Mathematics

Algebraic Geometry

9 pages

Scientific paper

We prove that for any pair of integers 0\leq r\leq g such that g\geq 3 or r>0, there exists a (hyper)elliptic curve C over F_2 of genus g and 2-rank r whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polarized abelian varieties (A,\lambda) over F_2 of dimension g and 2-rank r such that \Aut(A,\lambda)={\pm 1}.

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