A tower of complete moduli spaces of Calabi-Yau $n$-folds
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908904025227264 |
|---|---|
| author | Alexeev, Valery |
| author_facet | Alexeev, Valery |
| contents | We construct a sequence of complete moduli spaces $$E_0 \subset E_1 \subset E_2 \subset \dots E_n \subset\dots,$$ each of which is isomorphic to a weighted projective space. These spaces parameterize certain $n$-dimensional Calabi-Yau varieties associated with the Sylvester sequence $2,3,7,43,\dots$. They generalize the moduli space of elliptic curves $\overline{M}_{1,1}=\mathbb P(4,6)$ and Brieskorn's family over $\overline{F}^{\rm BB}_{U\oplus E_8} = \mathbb P(4,10,\dotsc, 42)$, the Baily-Borel compactification of the moduli space of $U\oplus E_8$-polarized K3 surfaces. We also study fibrations in such Calabi-Yau varieties, extending to higher dimensions the theory of elliptic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A tower of complete moduli spaces of Calabi-Yau $n$-folds Alexeev, Valery Algebraic Geometry 14D23, 14B07, 14J32 We construct a sequence of complete moduli spaces $$E_0 \subset E_1 \subset E_2 \subset \dots E_n \subset\dots,$$ each of which is isomorphic to a weighted projective space. These spaces parameterize certain $n$-dimensional Calabi-Yau varieties associated with the Sylvester sequence $2,3,7,43,\dots$. They generalize the moduli space of elliptic curves $\overline{M}_{1,1}=\mathbb P(4,6)$ and Brieskorn's family over $\overline{F}^{\rm BB}_{U\oplus E_8} = \mathbb P(4,10,\dotsc, 42)$, the Baily-Borel compactification of the moduli space of $U\oplus E_8$-polarized K3 surfaces. We also study fibrations in such Calabi-Yau varieties, extending to higher dimensions the theory of elliptic surfaces. |
| title | A tower of complete moduli spaces of Calabi-Yau $n$-folds |
| topic | Algebraic Geometry 14D23, 14B07, 14J32 |
| url | https://arxiv.org/abs/2511.16562 |