Decomposing Jacobians of Hyperelliptic Curves
نویسنده
چکیده
Many interesting questions can be asked about the decomposition of Jacobians of curves. For instance, we may want to know which curves have completely decomposable Jacobians (Jacobians which are the product of g elliptic curves) [4]. We may ask about number theoretic properties of the elliptic curves that show up in the decomposition of Jacobians of curves [2]. We would also like to know how many isogenous elliptic curve factors can occur in the decomposition of some curve for a given genus. Our goal in this paper is to decompose the Jacobians of hyperelliptic curves using information about groups of automorphisms acting on the curves. The decomposition in the genus 2 case is well known [6], [7]. We determine the decomposition of many hyperelliptic curves of genus 3 and 4.
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