Baily--Borel compactifications of period images and the b-semiampleness conjecture
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909968130637824 |
|---|---|
| author | Bakker, Benjamin Filipazzi, Stefano Mauri, Mirko Tsimerman, Jacob |
| author_facet | Bakker, Benjamin Filipazzi, Stefano Mauri, Mirko Tsimerman, Jacob |
| contents | We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map of a polarizable integral pure variation of Hodge structures for which the Griffiths bundle extends amply. In particular the Griffiths bundle is semiample. We prove more generally that the Hodge bundle of a Calabi--Yau variation of Hodge structures is semiample subject to some extra conditions, and as our second result deduce the b-semiampleness conjecture and the existence of a functorial Hodge-theoretic compactification of moduli spaces of polarized Calabi--Yau varieties. The semiampleness results (and the construction of the Baily--Borel compactifications) crucially use o-minimal GAGA, and the deduction of the b-semiampleness conjecture uses work of Ambro and results of Kollár on the geometry of minimal lc centers to verify the extra conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Baily--Borel compactifications of period images and the b-semiampleness conjecture Bakker, Benjamin Filipazzi, Stefano Mauri, Mirko Tsimerman, Jacob Algebraic Geometry Complex Variables Number Theory Primary: 14D07. Secondary: 14E30, 14C30, 14J10, 03C64 We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map of a polarizable integral pure variation of Hodge structures for which the Griffiths bundle extends amply. In particular the Griffiths bundle is semiample. We prove more generally that the Hodge bundle of a Calabi--Yau variation of Hodge structures is semiample subject to some extra conditions, and as our second result deduce the b-semiampleness conjecture and the existence of a functorial Hodge-theoretic compactification of moduli spaces of polarized Calabi--Yau varieties. The semiampleness results (and the construction of the Baily--Borel compactifications) crucially use o-minimal GAGA, and the deduction of the b-semiampleness conjecture uses work of Ambro and results of Kollár on the geometry of minimal lc centers to verify the extra conditions. |
| title | Baily--Borel compactifications of period images and the b-semiampleness conjecture |
| topic | Algebraic Geometry Complex Variables Number Theory Primary: 14D07. Secondary: 14E30, 14C30, 14J10, 03C64 |
| url | https://arxiv.org/abs/2508.19215 |