Double Kodaira fibrations
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Fabrizio Catanese
Abstract
The existence of a Kodaira fibration, i.e., of a fibration of a compact complex surface S onto a complex curve B which is a differentiable but not a holomorphic bundle, forces the geographical slope 
to lie in the interval (2, 3). But up to now all the known examples had slope ν(S) ≦ 2 + 1/3. In this paper we consider a special class of surfaces admitting two such Kodaira fibrations, and we can construct many new examples, showing in particular that there are such fibrations attaining the slope ν(S) = 2 + 2/3. We are able to explicitly describe the moduli space of such class of surfaces, and we show the existence of Kodaira fibrations which yield rigid surfaces. We observe an interesting connection between the problem of the slope of Kodaira fibrations and a ‘packing’ problem for automorphisms of algebraic curves of genus ≧ 2.
© Walter de Gruyter Berlin · New York 2009
Articles in the same Issue
- Groupoids and an index theorem for conical pseudo-manifolds
- Linear forms in elliptic logarithms
- Random quotients of the modular group are rigid and essentially incompressible
- The pro-p Hom-form of the birational anabelian conjecture
- Multiplication operators on the Bergman space via the Hardy space of the bidisk
- Morita equivalences of cyclotomic Hecke algebras of type G(r, p, n)
- Special correspondences and Chow traces of Landweber-Novikov operations
- Double Kodaira fibrations
Articles in the same Issue
- Groupoids and an index theorem for conical pseudo-manifolds
- Linear forms in elliptic logarithms
- Random quotients of the modular group are rigid and essentially incompressible
- The pro-p Hom-form of the birational anabelian conjecture
- Multiplication operators on the Bergman space via the Hardy space of the bidisk
- Morita equivalences of cyclotomic Hecke algebras of type G(r, p, n)
- Special correspondences and Chow traces of Landweber-Novikov operations
- Double Kodaira fibrations
