1. Construction and deformations of Calabi–Yau 3folds in codimension 4.
 Author

Mohsin, Sumayya, Nazir, Shaheen, and Qureshi, Muhammad Imran
 Subjects
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PROJECTIVE spaces , *GORENSTEIN rings , *ORBIFOLDS  Abstract
We construct polarized Calabi–Yau 3folds with at worst isolated canonical orbifold points in codimension 4 that can be described in terms of the equations of the Segre embedding of P 2 × P 2 in P 8. We investigate the existence of other deformation families in their Hilbert scheme by either studying Tom and Jerry degenerations or by comparing their Hilbert series with those of existing low codimension Calabi–Yau 3folds. Among other interesting results, we find a family of Calabi–Yau 3fold with five distinct Tom and Jerry deformation families, a phenomenon not seen for Q Fano 3folds. We compute the Hodge numbers of P 2 × P 2 Calabi–Yau 3folds and corresponding manifolds obtained by performing crepant resolutions. We obtain a manifold with a pair of Hodge numbers that does not appear in the famously known list of 30108 distinct Hodge pairs of Kruzer–Skarke, in the list of 7890 distinct Hodge pairs corresponding to complete intersections in the product of projective spaces and in Hodge paris obtained from Calabi–Yau 3folds having low codimension embeddings in weighted projective spaces. [ABSTRACT FROM AUTHOR]
 Published
 2024
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