A366650 Number of Calabi-Yau threefolds that are a complete intersection (CICY) in products of n projective spaces.

5, 44, 195, 552, 1186, 1804, 1917, 1363, 629, 166, 26, 3

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

Table of n, a(n) for n=1..12.

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

Cf. A331445, A366678.

Sequence in context: A173376 A364605 A128523 * A271298 A271118 A268762

Adjacent sequences: A366647 A366648 A366649 * A366651 A366652 A366653

Keyword

nonn,fini,full

Author

Charles R Greathouse IV, Oct 16 2023

Status

approved