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Threefolds fibred by mirror sextic double planes

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posted on 12.06.2020, 13:09 authored by Remkes Kooistra, Alan ThompsonAlan Thompson
We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic surfaces. We show that the geometry of such threefolds is controlled by a pair of invariants, called the generalized functional and generalized homological invariants, and we derive an explicit birational model for them, which we call the Weierstrass form. We then describe how to resolve the singularities of the Weierstrass form to obtain the "minimal form", which has mild singularities and is unique up to birational maps in codimension 2. Finally we describe some of the geometric properties of threefolds in minimal form, including their singular fibres, canonical divisor, and Betti numbers.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Canadian Journal of Mathematics

Volume

73

Issue

5

Pages

1305-1346

Publisher

Cambridge University Press

Version

AM (Accepted Manuscript)

Rights holder

© Canadian Mathematical Society

Publisher statement

This article has been published in a revised form in Canadian Journal of Mathematics https://doi.org/10.4153/S0008414X20000498. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Canadian Mathematical Society.

Acceptance date

08/06/2020

Publication date

2020-06-24

Copyright date

2021

Notes

35 pages, 16 figures. Comments welcome!

ISSN

0008-414X

Language

en

Depositor

Dr Alan Thompson. Deposit date: 11 June 2020

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