On hyperelliptic curves of genus 3

We study the moduli space of genus 3 hyperelliptic curves via the weighted projective space of binary octavics. This enables us to create a database of all genus 3 hyperelliptic curves defined over $\mathbb Q$, of weighted moduli height $\mathcal h =1$

On automorphisms of algebraic curves

An irreducible, algebraic curve $\mathcal X_g$ of genus $g\geq 2$ defined over an algebraically closed field $k$ of characteristic \mbox{char } \, k = p \geq 0, has finite automorphism group \mbox{Aut} (\mathcal X_g). In this paper we describe methods of determining the list of groups \mbox{Aut} (\mathcal X_g) for a fixed $g\geq 2$. Moreover, equations of the corresponding families of curves are given when possible