A Calabi-Yau object (Calabi-Yau manifold, Calabi-Yau category) of (complex) dimension 3.
Spin(8)-subgroups and reductions to exceptional geometry
reduction | from spin group | to maximal subgroup |
---|---|---|
Spin(7)-structure | Spin(8) | Spin(7) |
G2-structure | Spin(7) | G2 |
CY3-structure | Spin(6) | SU(3) |
SU(2)-structure | Spin(5) | SU(2) |
generalized reduction | from Narain group | to direct product group |
generalized Spin(7)-structure | $Spin(8,8)$ | $Spin(7) \times Spin(7)$ |
generalized G2-structure | $Spin(7,7)$ | $G_2 \times G_2$ |
generalized CY3 | $Spin(6,6)$ | $SU(3) \times SU(3)$ |
see also: coset space structure on n-spheres
moduli spaces of line n-bundles with connection on $n$-dimensional $X$
Discussion of intermediate Jacobians of Calabi-Yau 3-folds includes
C. Herbert Clemens, Phillip Griffith, The intermediate Jacobian of the cubic threefold, Annals of Mathematics Second Series, Vol. 95, No. 2 (Mar., 1972), pp. 281-356 (JSTOR)
Andreas Höring, Minimal classes on the intermediate Jacobian of a generic cubic threefold, 2008 (pdf)
Discussion of the Artin-Mazur groups? of CY3s in positive characteristic:
Discussion of motivic Hall algebras of CY 3-folds is in
Last revised on March 30, 2019 at 10:00:17. See the history of this page for a list of all contributions to it.