K3ModuliTalkNotes.pdf (536.21 kB)

The geometry and moduli of K3 surfaces

Download (536.21 kB)
journal contribution
posted on 08.10.2018, 12:32 by Andrew Harder, Alan Thompson
These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of polarized K3 surfaces, studying their moduli, degenerations and the compactification problem. This theory is then further enhanced to a discussion of lattice polarized K3 surfaces, which provide a rich source of explicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3 surfaces, and give some of their applications.

Funding

A. Harder was supported by an NSERC PGS D scholarship and a University of Alberta Doctoral Recruitment Scholarship. A. Thompson was supported by a Fields-Ontario-PIMS postdoctoral fellowship with funding provided by NSERC, the Ontario Ministry of Training, Colleges and Universities, and an Alberta Advanced Education and Technology Grant.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Fields Institute Monographs

Volume

34

Pages

3 - 43

Citation

HARDER, A. and THOMPSON, A., 2015. The geometry and moduli of K3 surfaces. IN: Laza, R., Schutt, M. and Yui, N. (eds.) Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Lecture Notes on Concentrated Graduate Courses. New York: Springer, pp. 3-43.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This is a pre-copyedited version of a contribution published in Laza, R., Schutt, M. and Yui, N. (eds.) Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Lecture Notes on Concentrated Graduate published by Springer. The definitive authenticated version is available online via https://doi.org/10.1007/978-1-4939-2830-9_1

ISBN

9781493928293

ISSN

1069-5273

eISSN

2194-3079

Book series

Fields Institute Monographs;34

Language

en

Exports

Logo branding

Keywords

Exports