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

Published online by Cambridge University Press:  20 November 2018

Marie-Amélie Bertin
Marie-Amélie Bertin*
Affiliation:
12 rue des Bretons, 94700 Maisons Alfort, France, e-mail: [email protected]
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Abstract

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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 $\rho =1$.

Keywords

14J3214Q15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 5 , 01 October 2009 , pp. 1050 - 1072
Copyright
Copyright © Canadian Mathematical Society 2009

References

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