Abstract

An elliptic K3 surface is a K3 surface with an elliptic fibration: a surjective morphism to P¹ whose generic fibre is a smooth genus 1 curve. We will discuss how geometric information such as automorphisms and double cover structures of an elliptic K3 surface can be extracted from examining the singular fibres and sections (if any) of its elliptic fibrations. At the end of the talk, we will mention a geometric realisation of certain torsion elements in the Tate-Shafarevich group, a group that parameterises elliptic fibrations with reduced fibres and the same relative Jacobian fibration. The talk will be kept intuitive with explicit pictorial examples.

 

Organizers: Kuan-Wei Chen (NCTS), Wille Liu (AS)