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Fibred surfaces and moduli. (English) Zbl 0778.14005

The author studies surjective morphisms \(\varphi:S\to C\) with connected fibers from a smooth projective surface \(S\) onto a smooth curve \(C\). He proves a criterion for isotriviality, i.e. constant isomorphism type of the fibers of \(\varphi\), in terms of the number of sections of tensor powers of the relative canonical sheaf of \(\varphi\). Furthermore generalizing a result of F. Catanese [Invent. Math. 104, No. 2, 263-289 (1991; Zbl 0743.32025)] he gives a bound for the dimension of \(H^ 1(S,T_ S)\) for an arbitrary nonisotrivial \(\varphi\).

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14J10 Families, moduli, classification: algebraic theory
14E99 Birational geometry

Citations:

Zbl 0743.32025
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References:

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