Math @ Duke
Publications [#318284] of Robert Bryant
- with Bryant, R; Griffiths, PA, Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle,
in Arithmetic and geometry, Vol. II, Progress in Mathematics, edited by Artin, M; Tate, J, vol. 36
pp. 77-102, Birkhäuser Boston, ISBN 3-7643-3133-X [MR86a:32044]
(last updated on 2017/12/14)
We examine the infinitesimal period relations of a
3-fold with trivial
canonical bundle and show that they represent an
system on the higher period domain that is the first
prolongation of a
contact system on a `de-prolonged' period domain.
This has some interesting
consequences for relations between the so called
A-periods and B-periods,
showing that they can be expressed in terms of a
single `potential' function.
Of course, in recent years, 3-folds with trivial
canonical bundle have
become a central part of string theory. The literature on
manifolds and their geometry and deformation theory
has seen an explosive
growth, which I am not competent to catalog. I would
suggest that you contact
my colleague, D. Morrison (firstname.lastname@example.org), if you
want pointers to
a survey article.
Reprints are available.
Duke University, Box 90320
Durham, NC 27708-0320