Gopakumar-Vafa Invariants for CICYs


This website was set up by Federico Carta, Alessandro Mininno, Nicole Righi and Alexander Westphal.

The original paper, explaining how the database was constructed, is available on ArXiv:2101.07272 (hep-th).

The algorithm used to compute the Gopakumar-Vafa invariants is reviewed in the paper and it is based on ArXiv:9308122 (hep-th) and ArXiv:9406055 (hep-th).

The following links are associated to a zip files containing the file for the Gopakumar-Vafa invariants up to degree 10 of all the non-product favorable CICYs at fixed h1,1.

The files for each CICY are named with the number associated to the CICY by the authors of ArXiv:1708.07907 (hep-th).

h1,1 = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

CICY redundancies


The original paper, explaining how the database was constructed, is available on ArXiv:2101.07272 (hep-th).

The following link is associated to a Mathematica notebook containing the matrix necessary for the transformation between two CICYs that are isomorphic among each other for Wall's theoreom. Such matrices have been found using the CICY database introduced in ArXiv:1708.07907 (hep-th). The notebook contains only a subset of all possible redundancies, and it does not contains all the CICYs that are trivially redundant. It is however possible to obtain all the transformation associated to all the redundant CICYs listed in ArXiv:2101.07272 (hep-th) by multiplication. The matrix is applied on the vector of the integrals of c2 on the divisor basis as given by ArXiv:1708.07907 and on the basis itself. The first component of the Mathematica notebook has the number of the CICY at which the matrix must be applied to get the isomorphic one. For explicit examples, we refer to ArXiv:2101.07272 (hep-th).

Redundant CICYs