K3ModuliTalkNotes.pdf (536.21 kB)
The geometry and moduli of K3 surfaces
journal contributionposted on 2018-10-08, 12:32 authored by Andrew Harder, Alan ThompsonAlan 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.
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.
- Mathematical Sciences
Published inFields Institute Monographs
Pages3 - 43
CitationHARDER, 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.
- AM (Accepted Manuscript)
Publisher statementThis 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/
NotesThis 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
Book seriesFields Institute Monographs;34