Let G be a finite group, and g â‰¥ 2. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves withâ€¦ (More)

In this note we discuss techniques for determining the automorphism group of a genus $g$ hyperelliptic curve $\X_g$ defined over an algebraically closed field $k$ of characteristic zero. The firstâ€¦ (More)

We study genus 2 function fields with elliptic subfields of degree 2. The locus L2 of these fields is a 2-dimensional subvariety of the moduli space M2 of genus 2 fields. An equation for L2 isâ€¦ (More)

In this paper we study genus 2 function fields K with degree 3 elliptic subfields. We show that the number of Aut(K)-classes of such subfields of fixed K is 0,1,2 or 4. Also we compute an equationâ€¦ (More)

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problemsâ€¦ (More)

Let X be an algebraic curve of genus g â‰¥ 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code CX . When this code (or itsâ€¦ (More)

Let X be an algebraic curve of genus g > 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code C. If the code C isâ€¦ (More)

We introduce a new approach of computing the automorphism group and the field of moduli of points p = [C] in the moduli space of hyperel-liptic curves Hg. Further, we show that for every moduli pointâ€¦ (More)

In the process of computing the Galois group of a prime degree polynomial f (x) over Q we suggest a preliminary checking for the existence of non-real roots. If f (x) has non-real roots, thenâ€¦ (More)

Applicable Algebra in Engineering, Communicationâ€¦

2006

We study genus g hyperelliptic curves with reduced automorphism group A 5 and give equations y 2Â =Â f(x) for such curves in both cases where f(x) is a decomposable polynomial in x 2 or x 5. For anyâ€¦ (More)