Keywords. Gromov-Witten invariants, rational and ruled algebraic surfaces, rational and ruled symplectic 4-manifolds, tropical enumerative geometry
AMS subject classification. Primary: 14N35. Secondary: 14J26, 53D45.
Submitted to GT on 30 December 2004. Paper accepted 25 March 2005. Paper published 7 April 2005.
Ilia Itenberg, Viatcheslav Kharlamov and Eugenii Shustin
(II and VK) Universite Louis Pasteur et IRMA, 7, rue Rene Descartes
67084 Strasbourg Cedex, France
(ES) School of Mathematical Sciences, Tel Aviv University
Ramat Aviv, 69978 Tel Aviv, Israel
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