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On Rational Elliptic Surfaces with Mordell-Weil Group of Rank Five

Davide FusiAndrea Luigi Tironi — 2010

Bollettino dell'Unione Matematica Italiana

Let E ( K ) be the Mordell-Weil group of a rational elliptic surface and let r be its rank. In this note we classify all the rational elliptic surfaces with Mordell-Weil group of rank r = 5 over an algebraically closed field of arbitrary characteristic and using the theory of Mordell-Weil lattices, we find systems of generators for E ( K ) in the coordinate-free situation.

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