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Journal of the London Mathematical Society 2001 63(2):288-298; doi:10.1017/S0024610700001824
© 2001 by London Mathematical Society
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© The London Mathematical Society

Jacobiennes de Courbes Algébriques de Genre 2 et 3 de Grand Rang Sur Q

Leopoldo Kulesz

UFR de Mathématiques, Université Paris 7 2 place Jussieu, F-75251 Paris Cedex 05, France, kulesz{at}math.jussieu.fr

Received 17 February 1999. Revision received 12 August 1999.

Infinite families of curves are constructed of genus 2 and 3 over Q whose jacobians have high rank over Q. More precisely, if E is an elliptic curve with rank at least r over Q, an infinite family of curves are constructed of genus 2 whose jacobians have rank at least r+4 over Q, and, under certain conditions, an infinite family of curves are constructed of genus 3 whose jacobians have rank at least 2r over Q. On specialisation, a family of curves are obtained of genus 2 whose jacobians have rank at least 27 and a family of curves are obtained of genus 3 whose jacobians have rank at least 26; one of these has rank at least 42.


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