Serrano, Fernando2020-03-032020-03-031989https://hdl.handle.net/2445/151842Preprint enviat per a la seva publicació en una revista científica: Pacific Journal of Mathematics, Volume 152, Number 1 (1992), 187-199.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.x p.application/pdfeng(c) Fernando Serrano, 1989Superfícies (Matemàtica)Universitat de Barcelona. Institut de Matemàticainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess