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Title: Lines on intersections of three quadrics
Author: Vincent, Ian
ISNI:       0000 0004 6348 5893
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2016
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In this document we formulate and discuss conjecture 1.2.1, giving an upper bound for the number of lines on K3 surfaces occurring as complete intersections of three quadrics in P5. In the case that these quadrics contain in their span a quadric of rank 4, we construct a pair of elliptic fibrations, each of which realises the lines on the surface as either sections or line components within the singular fibres, and the general fibre is realised as an intersection of two quadrics in P3. The possibilities for singular fibres are limited by the Euler number of the surface, while the rank of the group of sections is bounded by the rank of its Picard group. In the cases where this rank is low, these bounds are enough to prove the stated conjecture in the torsion-free case by utilising the height-pairing. In the remaining cases, if a surface has more lines than the stated conjecture, we discuss how these techniques can be used to construct necessary conditions on the configurations of the lines on the surface, along with an example of how this could work in practice.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics