CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

  Published:2012-09-21
 Printed: Aug 2013
  • Alan Thompson,
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada, T6G 2G1
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.
Keywords: threefold, fibration, K3 surface threefold, fibration, K3 surface
MSC Classifications: 14J30, 14D06, 14E30, 14J28 show english descriptions $3$-folds [See also 32Q25]
Fibrations, degenerations
Minimal model program (Mori theory, extremal rays)
$K3$ surfaces and Enriques surfaces
14J30 - $3$-folds [See also 32Q25]
14D06 - Fibrations, degenerations
14E30 - Minimal model program (Mori theory, extremal rays)
14J28 - $K3$ surfaces and Enriques surfaces
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/