M1FibredThreefolds.pdf (627.68 kB)
Threefolds fibred by mirror sextic double planes
journal contributionposted on 2020-06-12, 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.
- Mathematical Sciences
Published inCanadian Journal of Mathematics
PublisherCambridge University Press
- AM (Accepted Manuscript)
Rights holder© Canadian Mathematical Society
Publisher statementThis 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.
Notes35 pages, 16 figures. Comments welcome!