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Title: Elliptic surfaces with an ample divisor of genus two
Author: Serrano, Fernando
Keywords: Superfícies (Matemàtica)
Universitat de Barcelona. Institut de Matemàtica
Issue Date: 1989
Publisher: Universitat de Barcelona
Series/Report no: Mathematics Preprint Series; 69
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.
Note: Preprint enviat per a la seva publicació en una revista científica: Pacific Journal of Mathematics, Volume 152, Number 1 (1992), 187-199.
Note: Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 32.10]
Appears in Collections:Preprints de Matemàtiques - Mathematics Preprint Series

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