To put this question into its proper perspective, it may be useful to recall the following facts (cf. [Ka] for more details and historical remarks). If a curve C of genus 2 admits any non-constant morphism f 1 : C Γ E 1 to an elliptic curve E 1 at all in which case we say (mainly for historical reas
The number of genus 2 covers of an elliptic curve
β Scribed by Ernst Kani
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 342 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0025-2611
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Our main result is that a 1971 conjecture due to Paul Kainen is false. Kainen's conjecture implies that the genus 2 crossing number of K 9 is 3. We disprove the conjecture by showing that the actual value is 4. The method used is a new one in the study of crossing numbers, involving proof of the imp
We exhibit a genus-2 curve C defined over QΓ°TΓ which admits two independent morphisms to a rank-1 elliptic curve defined over QΓ°TΓ: We describe completely the set of QΓ°TΓ-rational points of the curve C and obtain a uniform bound on the number of Q-rational points of a rational specialization C t of