Hurwitz spaces of genus 2 covers of an elliptic curve
نویسنده
چکیده
Let E be an elliptic curve over a field K of characteristic 6= 2 and let N > 1 be an integer prime to char(K). The purpose of this paper is to study the family of genus 2 covers of E of fixed degree N , i.e. those covers f : C → E for which C/K is a curve of genus 2 and deg(f) = N . Since we can (without loss of generality) restrict our attention those covers that are normalized in the sense of section 2, this investigation is essentially equivalent to the study of the set
منابع مشابه
Equations for the Genus 2 Covers of Degree 3 of an Elliptic Curve Jan
E. Kani [4] has shown that the Hurwitz functor H E/K,3 , which parameter-izes the (normalized) genus 2 covers of degree 3 of one elliptic curve E over a field K, is representable. In this paper the moduli scheme H E/k,3 and the universal family are explicitly calculated over an algebraically closed field k and described by short equations.
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تاریخ انتشار 2001