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

D.B.A. Epstein

• 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.