calabi-yau-coni-pfvs

Number of PFVs found for various conifolds, found via pfvs.

This dataset holds both the data necessary to run the pfv code (intersection numbers kappa_coo, second chern class c2, hyperplanes H) and the resultant PFVs (M, K).

The PFV runs have configuration, primarily in the number of p-vectors studied and the maximum dilation considered. These are parameterized PFV-by-PFV using pfv_infnorm and pfv_reqdil respectively. There is also larger-scale information like the number of PFVs found npfvs, the number of p-vectors studied frontier_npvecs, how large of a box of PFVs this corresponds to frontier_infnorm, and the dilation used for the PFV searches frontier_dil.

The count of PFVs at any (B', dil') within a stored frontier is #{i : pfv_infnorm[i] <= B' and pfv_reqdil[i] <= dil'}.

One row per conifold: 18,253 conifolds, 417 polytopes, 814,034 PFVs.

Columns

Order is

h11, h21, polyID, classID, coniID, # coni specification
kappa_coo, c2, H,                  # coni relevant data
M, K, pfv_infnorm, pfv_reqdil,     # PFV-level data
npfvs, frontier_npvecs, frontier_infnorm, frontier_dil # search-level data

column	dtype	notes
h11	int32	Hodge number h^{1,1}
h21	int32	Hodge number h^{2,1}
polyID	int64	polytope ID
classID	int32	class ID
coniID	int32	conifold ID
kappa_coo	list[list[int64]]	intersection numbers, sparse [i, j, k, value] (upper triangle)
c2	list[int64]	second Chern class
H	list[list[int64]]	hyperplanes
M	list[list[int64]]	PFV M-vectors
K	list[list[int64]]	PFV K-vectors
pfv_infnorm	list[int64]	per-PFV p-vector infinity norm
pfv_reqdil	list[int64]	per-PFV required dilation
npfvs	int64	number of PFVs found
frontier_npvecs	list[int64]	number of p-vectors studied, per search setting
frontier_infnorm	list[int64]	box bound B, per search setting
frontier_dil	list[int64]	dilation, per search setting