Publications [#9581] of Robert Bryant

Papers Published

1. with Phillip A. Griffiths, 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 Michael Artin and John Tate, vol. 36 (1983), pp. 77–102, Birkhäuser Boston, Boston, MA [MR86a:32044]
   (last updated on 2004/04/06)

   Author's Comments:
   We examine the infinitesimal period relations of a 3-fold 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 `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 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.