Moduli of rational fibrations

Details Moduli of rational fibrations Moduli of rational fibrations

2007-02-28

arxiv.org/abs/math/0702865v2

Mathematics

Algebraic Geometry

34 pages. The results of version 1 have been extended to nodal curves and the requirement that the special fibres of the fibra

Scientific paper

We prove results implying, under mild restrictions, the upper bound 19 for the geometric genus of a nodal irreducible curve whose normalization has general moduli and varying in a non-trivial linear system of curves of the same geometric genus on some non-ruled surface. This gives some evidence for the non-uniruledness of the moduli spaces of stable curves of genus 20 and 21. The proofs use deformation theory of surfaces fibered over the projective line.

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