Terminal Fano 4-Folds (codim 2 & 3) — Searchable Data

A client-side searchable catalogue of terminal Fano 4-fold weighted complete intersections (codimension 2 and 3). Filter by W (sum of ambient weights), basket size, type (K0, K1, K2, CY3), and the invariant (−KX)4.

W is defined as W := ∑ wi, the sum of the ambient weights. In this dataset, W ≤ 121 for codimension 2 and W ≤ 81 for codimension 3 (bounds used in the accompanying paper).

Results

0 matches
Data provided by Imran Qureshi.
Type definitions (tap to expand): K0 / K1 / K2 / CY3

Let X be an index-1 isolated terminal Fano 4-fold and |−KX| its anticanonical linear system.

  • K0: |−KX| is empty (equivalently h0(−KX) = 0), so X has no anticanonical divisor and hence no anticanonical Calabi–Yau 3-fold section.
  • K1: h0(−KX) = 1, but the unique anticanonical member Y ∈ |−KX| is not a quasismooth Calabi–Yau 3-fold with isolated canonical orbifold points.
  • K2: h0(−KX) ≥ 2, but a general member Y ∈ |−KX| is not a quasismooth Calabi–Yau 3-fold with isolated canonical orbifold points.
  • CY3: the family admits an anticanonical section Y ∈ |−KX| that is a quasismooth Calabi–Yau 3-fold with isolated canonical orbifold points.

“Basket” means the multiset of orbifold singularity types recorded for X; the “basket size” is the total count (including multiplicities).

ID Codim Weights Degrees (−KX)4 Basket (terms) Type
Tip: click a basket cell to copy its text.