Spaces of sections of quadric surface fibrations over curves

Details Spaces of sections of quadric surface fibrations over curves Spaces of sections of quadric surface fibrations over curves

2011-11-04

arxiv.org/abs/1111.1203v1

Mathematics

Algebraic Geometry

23 pages; to appear in the proceedings of the 2010 conference 'Compact Moduli and Vector Bundles', held at the University of G

Scientific paper

We consider quadric surface fibrations over curves, defined over algebraically closed and finite fields. Our goal is to understand, in geometric terms, spaces of sections for such fibrations. We analyze varieties of maximal isotropic subspaces in the fibers as P^1-bundles over the discriminant double cover. When the P^1-bundle is suitably stable, we deduce effective estimates for the heights of sections over finite fields satisfying various approximation conditions. We also discuss the behavior of the spaces of sections as the base of the fibration acquires singularities.

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