2020/04/20 by Tüli̇n Altunöz, Tulin Altunoz
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #math.GT
paper · pdf · doi:10.2969/jmsj/82988298
published as J. Math. Soc. Japan Advance publication (2020) · 15 pages
arxiv created 2020/04/20 · openalex publication_date 2020/08/17 · arxiv updated 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider complex surfaces, viewed as smooth 4-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the 2-sphere. In this paper, we show that the minimal number of singular fibers of such fibrations is equal to 2g+4 for even g≥4. For odd g≥7, we show that the number is greater than or equal to 2g+6. Moreover, we discuss the minimal number of singular fibers in all hyperelliptic Lefschetz fibrations over the 2-sphere as well.