Abstract
We study the geometry of $3$-codimensional smooth subvarieties of the complex projective space. In particular, we classify all quasi-Buchsbaum Calabi--Yau threefolds in projective $6$-space. Moreover, we prove that this classification includes all Calabi--Yau threefolds contained in a possibly singular 5-dimensional quadric as well as all Calabi--Yau threefolds of degree at most $14$ in $\mathbb{P}^6$.
Highlights
It is conjectured that, when 2n ≥ N, there is a finite number of smooth families of smooth n-dimensional subvarieties of PN that are not of general type
We study nondegenerate Calabi–Yau threefolds, i.e., such Calabi–Yau threefolds which are not contained in any hyperplane
We prove a technical result (Proposition 7.2) on deformation of Pfaffian varieties implying that any threefold B14 ∈ B14 appears as a smooth degeneration of the family T14 of Calabi–Yau threefolds defined by 6 × 6 Pfaffians of alternating 7 × 7 matrices of linear forms
Summary
It is conjectured that, when 2n ≥ N , there is a finite number of smooth families of smooth n-dimensional subvarieties of PN that are not of general type. We prove that all Calabi–Yau threefolds of degree at most 14 in P6 are quasi-Buchsbaum and use the classification of the latter threefolds contained in Sect. We prove a technical result (Proposition 7.2) on deformation of Pfaffian varieties implying that any threefold B14 ∈ B14 appears as a smooth degeneration of the family T14 of Calabi–Yau threefolds defined by 6 × 6 Pfaffians of alternating 7 × 7 matrices of linear forms This proves that all families of Calabi–Yau threefolds of degree 14 which appear in the classification of Sect. Prove that the examples of degree 15 constructed in [7] are not smooth but admits three ordinary double points
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
