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On the arithmetic of the hyperelliptic curve y 2 = x n + a

Kevser Aktaş, Hasan Şenay (2016)

Czechoslovak Mathematical Journal

We study the arithmetic properties of hyperelliptic curves given by the affine equation y 2 = x n + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps).

On the Difference of 4-Gonal Linear Systems on some Curves

Ohbuchi, Akira (1997)

Serdica Mathematical Journal

Let C = (C, g^1/4 ) be a tetragonal curve. We consider the scrollar invariants e1 , e2 , e3 of g^1/4 . We prove that if W^1/4 (C) is a non-singular variety, then every g^1/4 ∈ W^1/4 (C) has the same scrollar invariants.

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