Pencils of genus two curves on rational surfaces

2010/06/22 by Shinya Kitagawa, Kitagawa, Shinya · 1 citation
Mathematics · Computer Science · Engineering · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1006.4372

Abstract

We consider relatively minimal fibrations of curves of genus two on rational surfaces whose Picard numbers are not maximal. By birational morphisms, such fibred surfaces are interpreted as pencils of plane curves. We show that only four are canonical, among a variety of possible models. For each canonical pencil, we give an example with trivial Mordell-Weil group.

Cited by

• Arithmetic rank bounds for abelian varieties over function fields

Related

• A new class of surfaces with maximal Picard number
• Extremal hyperelliptic fibrations on rational surfaces
• Birational automorphisms of algebraic varieties with a pencil of cubic surfaces
• Genus 2 pencils on surfaces with p_g=K²=1, envelopes, and conics tangent to plane cubic curves
• Towards the classification of semistable fibrations having exactly five singular fibers