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

Bertin, Marie-Amélie

Canadian journal of mathematics, Tome 61 (2009) no. 5, pp. 1050-1072

Résumé

We give some examples of Calabi–Yau 3-folds with $\rho =1$ and $\rho =2$ , defined over $\mathbb{Q}$ and constructed as 4-codimensional subvarieties of ${{\mathbb{P}}^{7}}$ via commutative algebra methods. We explain how to deduce their Hodge diamond and top Chern classes from computer based computations over some finite field ${{\mathbb{F}}_{p}}$ . 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–Negård and Kustin–Miller complexes of locally free sheaves.Finally, we give two new examples of Calabi–Yau 3-folds of ${{\mathbb{P}}^{6}}$ of degree 14 and 15 (defined over $\mathbb{Q}$ ). 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 $({{H}^{3}},{{c}_{2}}\cdot H,{{c}_{3}})$ and $\rho =1$ .

Détail

DOI : 10.4153/CJM-2009-050-2

Mots-clés : 14J32, 14Q15

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