Let $\cX$ be a curve of genus $g\ge2$ and zero $p$-rank over an algebraically closed field of odd characteristic $p$. We classify the pairs $(\cX,G)$ for which $G\le\Aut(\cX)$ has no common fixed point and $|G|>24g(g-1)$. For $g\ge4$, the curves are explicit cyclic covers of the projective line, the Hermitian curve, or...
Let $k$ be an algebraically closed field of characteristic $2$ and let $q=2^h$, $h\ge3$. We construct ordinary bielliptic curves $X$ of genus $q+1$ for which \[ \Aut(X)\cong \Dih(C_q)\times C_2, \qquad |\Aut(X)|=4q=4(g(X)-1). \] These curves realize case \textup{(ib)} in the classification of Giulietti--Korchm\'aros an...
Let $q=p^h$ be an odd prime power and let $X/\F_{q^2}$ be a maximal curve of genus at least two. We classify the curves for which the full geometric automorphism group is transitive on the set of $\F_{q^2}$-rational points. We prove that, if $h>1$, then $X$ is the Hermitian curve. If $h=1$, the only additional possibil...
We study algebraic geometry codes on hyperelliptic curves of genus $g \geq 2$ with complementarity properties. Our first contribution is a characterization of non-special divisors of degree $g$ and $g-1$ via the polynomial degrees of their reduced Mumford representation, reducing a classical hard geometric problem to a...
Adler V. Marques, Yuri da Silva, Saeed Tafazolian· arXiv.org· 0 citations
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