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Families of K3 surfaces polarised by a rank 18 lattice

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posted on 2024-07-03, 10:48 authored by Joseph Prebble

We study families of K3 surfaces polarised by a particular rank 18 lattice composed of one copy of the hyperbolic lattice and two copies of the (unique) even negative definite unimodular lattice of rank 8. We determine the normal form of a threefold to which all such families are birational over a base. Singular  fibres of these families then correspond to geometric conditions over the moduli space for such surfaces. We exhibit the families with central fibre set to be singular under various conditions and determine how one can arrive at different projective models for these families and thus attain different Tyurin degenerations.

Funding

EPSRC

Koja

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

Loughborough University

Rights holder

© Joseph Prebble

Publication date

2023

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy of Loughborough University.

Language

  • en

Supervisor(s)

Alan Thompson ; Evgeny Ferapontov ; Hamid Abban

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