The minimal number of singular fibers of a semistable curves over P1
Sheng-Li Tan
Abstract
In this paper, we shall prove Beauville's conjecture: if f:S P1 is a non-trivial semistable fibration of genus g>1, then f admits at least 5 singular fibers. We have also constructed an example of genus 2 with 5 singular fibers. This paper will appear in the Journal of Algebraic Geometry.
Create a lesson
Related papers
Complements on surfaces
V. V. Shokurov
Isolated rational curves on K3-fibered Calabi-Yau threefolds
Torsten Ekedahl, Trygve Johnsen, Dag Einar Sommervoll
Cohomology of complete intersections in toric varieties
Anvar R. Mavlyutov
The Gross-Kohnen-Zagier theorem in higher dimensions
Richard E. Borcherds
Real deformations and complex topology of plane curve singularities
Norbert A'Campo
Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves
Tomas L. Gomez