OFFSET
1,1
COMMENTS
A CICY is a Calabi-Yau threefold that is a complete intersection in products of projective spaces.
There are a(1) + a(2) + ... + a(12) = 7890 CICYs in total.
a(1) = 5 corresponds to the five terms in A331445.
LINKS
Jiakang Bao, Yang-Hui He, Edward Hirst, and Stephen Pietromonaco, Lectures on the Calabi-Yau Landscape, arXiv preprint (2020). arXiv:2001.01212 [hep-th]
Volker Braun, On Free Quotients of Complete Intersection Calabi-Yau Manifolds, arXiv preprint (2010). arXiv:1003.3235 [hep-th]
P. Candelas, A. M. Dale, C. A. Lutken, and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nuclear Physics B 298.3 (1988), pp. 493-525.
University of Oxford Department of Physics, The List of Complete Intersection Calabi-Yau Three-Folds
EXAMPLE
There are 5 CICYs in projective space: one with a single polynomial (degree 5, the quintic), two with two polynomials (degrees 2,4 and 3,3), one with three polynomials (degrees 2,2,3), and one with four polynomials (degrees 2,2,2,2), hence a(1) = 5.
There are 44 CICYs in the direct product of two projective spaces, hence a(2) = 44.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Charles R Greathouse IV, Oct 16 2023
STATUS
approved