A Functional Relation for Accessory Parameters for Genus 2 Algebraic Curves with an Order 4 Automorphism |
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Authors: | Silhol Robert |
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Institution: | Département de Mathématiques, UMR CNRS 5149, Université Montpellier II Place E. Bataillon, 34095 Montpellier Cedex 5, France, rs{at}math.univ-montp2.fr |
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Abstract: | Let C be a genus 2 algebraic curve defined by an equation ofthe form y2 = x(x2 1)(x a)(x 1/a). Asis well known, the five accessory parameters for such an equationcan all be expressed in terms of a and the accessory parameter b corresponding to a. The main result of the paper is thatif a' = 1 a2, which in general yields a non-isomorphiccurve C', then b'a'(a'2 1) = ba(a2 1). This is proven by it being shown how the uniformizing functionfrom the unit disk to C' can be explicitly described in termsof the uniformizing function for C. |
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