Examples of Calabi-Yau 3-Folds of P7 with ρ=1

We give some examples of Calabi-Yau 3-folds with rho = 1 and rho = 2, defined over Q and constructed as 4-codimensional subvarieties of P-7 via commutative algebra methods. We explain how to deduce their Hodge diamond and top Chern classes from computer based computations over some finite field F-p. Three of our examples (of degree 17 and 20) are new. The two others (degree 15 and 18) are known, and we recover their well-known invariants with our method. These examples are built out of Gulliksen-Negard and Kustin-Miller complexes of locally free sheaves. Finally, we give two new examples of Calabi-Yau 3-folds of P-6 of degree 14 and 15 (defined over Q). We show that they are not deformation equivalent to Tonoli's examples of the same degree, despite the fact that they have the same invariants (H-3, c(2) . H, c(3)) and rho = 1.