%I #26 Oct 16 2023 16:11:29
%S 5,44,195,552,1186,1804,1917,1363,629,166,26,3
%N Number of Calabi-Yau threefolds that are a complete intersection (CICY) in products of n projective spaces.
%C A CICY is a Calabi-Yau threefold that is a complete intersection in products of projective spaces.
%C There are a(1) + a(2) + ... + a(12) = 7890 CICYs in total.
%C a(1) = 5 corresponds to the five terms in A331445.
%H Jiakang Bao, Yang-Hui He, Edward Hirst, and Stephen Pietromonaco, <a href="https://arxiv.org/abs/2001.01212">Lectures on the Calabi-Yau Landscape</a>, arXiv preprint (2020). arXiv:2001.01212 [hep-th]
%H Volker Braun, <a href="https://arxiv.org/abs/1003.3235">On Free Quotients of Complete Intersection Calabi-Yau Manifolds</a>, arXiv preprint (2010). arXiv:1003.3235 [hep-th]
%H P. Candelas, A. M. Dale, C. A. Lutken, and R. Schimmrigk, <a href="https://cds.cern.ch/record/178648/files/198706385.pdf">Complete intersection Calabi-Yau manifolds</a>, Nuclear Physics B 298.3 (1988), pp. 493-525.
%H University of Oxford Department of Physics, <a href="https://www-thphys.physics.ox.ac.uk/projects/CalabiYau/cicylist/">The List of Complete Intersection Calabi-Yau Three-Folds</a>
%e 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.
%e There are 44 CICYs in the direct product of two projective spaces, hence a(2) = 44.
%Y Cf. A331445, A366678.
%K nonn,fini,full
%O 1,1
%A _Charles R Greathouse IV_, Oct 16 2023