Genus 2 curves that admit a degree 5 map to an elliptic curve
نویسندگان
چکیده
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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We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the " basic construction " of genus 2 covers of relative elliptic curves determine the cover in a unique way (up to isomorphism). A classical theorem says that a genus 2 cover of an elliptic curve of deg...
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The main aim of this paper is to determine the number cN,D of genus 2 covers of an elliptic curve E of fixed degree N ≥ 1 and fixed discriminant divisor D ∈ Div(E). In the case that D is reduced, this formula is due to Dijkgraaf. The basic technique here for determining cN,D is to exploit the geometry of a certain compactification C = CE,N of the universal genus 2 curve over the Hurwitz space H...
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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...
متن کاملFamilies of elliptic curves with genus 2 covers of degree 2
We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the ”basic construction” of genus 2 covers of relative elliptic curves determine the cover in a unique way (up to isomorphism). A classical theorem says that a genus 2 cover of an elliptic curve of degre...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2009
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum.2009.027