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1989

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/151842

Elliptic surfaces with an ample divisor of genus two

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Abstract

Beltrametti, Lanteri and Palleschi have recently started the classification of smooth algebraic surfaces having an ample divisor of arithmetic genus two (Arkiv für Mat. 25 (1987), 189-210). Their results for the class of elliptic surf aces can be considerably improved. The present paper focuses on elliptic surfaces S with Kodaira dimension one, xOs = O, and such that the (unique) elliptic fibration has a rational base. The result is the following : if S contains a genus two ample divisor then S is of the form S = (D x E)/G where G is a group acting on two curves D and E, E is elliptic, G is either Z2 x Z2 , Z2 x Z6 or Z4 x Z4 and D has genus 2,2 and 3 respectively. Moreover, the existence of such polarized surfaces is shown by a concrete example.

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Preprint enviat per a la seva publicació en una revista científica: Pacific Journal of Mathematics, Volume 152, Number 1 (1992), 187-199.

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Superfícies (Matemàtica)

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Universitat de Barcelona. Institut de Matemàtica

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Preprints de Matemàtiques - Mathematics Preprint Series

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SERRANO, Fernando. Elliptic surfaces with an ample divisor of genus two. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/151842

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