Free curves on varieties

Thesis

In this thesis we study various ways in which every two general points on a variety can be connected by curves of a fixed genus, thus mimicking the notion of a rationally connected variety but for arbitrary genus. We assume the existence of a covering family of curves which dominates the product of a variety with itself either by allowing the curves in the family to vary in moduli, or by assuming the family is trivial for some fixed curve of genus g. A suitably free curve will be one with a ...

Expand abstract

Authors: Gounelas, F

• Publication date: 2012
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: etale fundamental groups; rationally connected varieties; vector bundles on curves; free curves
• Subjects: Algebraic geometry; Number theory