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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00041 |
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| _version_ | 1866929609263546368 |
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| author | Imaike, Dai |
| author_facet | Imaike, Dai |
| contents | A Calabi-Yau 4-fold of Camere-Garbagnati-Mongardi is a crepant resolution of the quotient of a hyperkähler 4-fold by an antisymplectic involution. In this paper, we compare two different types of holomorphic torsion invariants; one is the BCOV invariant of the Calabi-Yau 4-fold of Camere-Garbagnati-Mongardi, and the other is the invariant of the corresponding $K3^{[2]}$-type manifold with involution introduced by the author in the preceding papers. As an application, in some special cases, we show that the BCOV invariant of those Calabi-Yau 4-folds is expressed as the Petersson norm of a certain Borcherds product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, III: relation with the BCOV invariant Imaike, Dai Algebraic Geometry A Calabi-Yau 4-fold of Camere-Garbagnati-Mongardi is a crepant resolution of the quotient of a hyperkähler 4-fold by an antisymplectic involution. In this paper, we compare two different types of holomorphic torsion invariants; one is the BCOV invariant of the Calabi-Yau 4-fold of Camere-Garbagnati-Mongardi, and the other is the invariant of the corresponding $K3^{[2]}$-type manifold with involution introduced by the author in the preceding papers. As an application, in some special cases, we show that the BCOV invariant of those Calabi-Yau 4-folds is expressed as the Petersson norm of a certain Borcherds product. |
| title | Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, III: relation with the BCOV invariant |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.00041 |