The minimal number of singular fibers of a semistable curves over P¹

1994/11/08 by Sheng-Li Tan, Tan, Sheng-Li · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9411002

6 pages, AmSTeX

arxiv created 1994/11/08 · openalex publication_date 1994/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves
• On Shimura curves in the Torelli locus of curves

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