Math @ Duke

Publications [#318284] of Robert Bryant
search www.ams.org.Papers Published
 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
(1983),
pp. 77102, BirkhĂ¤user Boston, ISBN 376433133X [MR86a:32044]
(last updated on 2018/08/20)
Author's Comments: We examine the infinitesimal period relations of a
3fold with trivial
canonical bundle and show that they represent an
exterior differential
system on the higher period domain that is the first
prolongation of a
contact system on a `deprolonged' period domain.
This has some interesting
consequences for relations between the so called
Aperiods and Bperiods,
showing that they can be expressed in terms of a
single `potential' function.
Of course, in recent years, 3folds with trivial
canonical bundle have
become a central part of string theory. The literature on
these complex
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 (drm@math.duke.edu), if you
want pointers to
a survey article.
Reprints are available.


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