Resumen de A functional relation for accessory parameters for genus 2 algebraic curves with an order 4 automorphism

Robert Silhol

• Let be a genus 2 algebraic curve defined by an equation of the form . As is well known, the five accessory parameters for such an equation can all be expressed in terms of and the accessory parameter corresponding to . The main result of the paper is that if , which in general yields a non-isomorphic curve , then .

  This is proven by it being shown how the uniformizing function from the unit disk to can be explicitly described in terms of the uniformizing function for.