The logarithmic spiral: a counterexample to the K=2 conjecture

• Autores: D.B.A. Epstein
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 161, Nº 2, 2005, págs. 925-957
• Idioma: inglés
• DOI: 10.4007/annals.2005.161.925
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• Resumen

  • We prove that any genus-2 Lefschetz fibration without reducible fibers and with ¡°transitive monodromy¡± is holomorphic. The latter condition comprises all cases where the number of singular fibers ¿Ì ¡Ê 10N is not congruent to 0 modulo 40. This proves a conjecture of the authors in [SiTi1]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S2-bundles over S2, of relative degree ¡Ü 7 over the base, and of symplectic surfaces in CP2 of degree ¡Ü 17.