Abstract
It is well-known that, aside from algebraic curves, abelian varieties, and a few other isolated cases such as K3 surfaces, the period matrices of a family of algebraic varieties satisfy non-trivial universal infinitesimal period relations. In this note we shall discuss some remarkable properties of any local solution to the differential system given by the infinitesimal period relation associated to polarized Ilodge structures of weight three with Ilodge number h 3,0 = 1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Bryant, Every compact Riemann surface may be immersed con-formally and minimally in S4, to appear in Dec. (1982) issue of Jour. Diff. Geom.
R. Bryant, S.S. Chern, and P. Griffiths, Exterior differential systems, Proc. Beijing Symposium, China Press (1982).
J. Carlson and P. Griffiths, Infinitesimal variation of Hodge structure and the global Torelli problem, Journees de geometric algebrique d’Angers, Sijthoff and Nordhoff (1980), pp. 51–76.
R. Donagi, The generic global Torelli theorem for most smooth hypersurfaces, to appear in Compositio Math.
A. Piateski-Shapiro and I. Shafarevich, A. Torelli theorem for algebraic surfaces of type K3, Isv. A.ad, Nauk., vol. 35 (1971), pp. 530–572.
Transcendental topics in algebraic geometry (Proceedings of the IAS Seminar 1981/82), P. Griffiths editor, to apper as an Annals of Math Studies.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bryant, R.L., Griffiths, P.A. (1983). Some Observations on the Infinitesimal Period Relations for Regular Threefolds with Trivial Canonical Bundle. In: Artin, M., Tate, J. (eds) Arithmetic and Geometry. Progress in Mathematics, vol 36. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-9286-7_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9286-7_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3133-8
Online ISBN: 978-1-4757-9286-7
eBook Packages: Springer Book Archive