Fano 4-folds with $b_2>12$ are products of surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916088824987648 |
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| author | Casagrande, Cinzia |
| author_facet | Casagrande, Cinzia |
| contents | Let X be a smooth, complex Fano 4-fold, and rho(X) its Picard number. We show that if rho(X)>12, then X is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial elementary contractions f: X->Y such that the image S of the exceptional divisor is a surface, together with the author's previous work on Fano 4-folds. In particular, given f: X->Y as above, under suitable assumptions we show that S is a smooth del Pezzo surface with -K_S given by the restriction of -K_Y. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11953 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fano 4-folds with $b_2>12$ are products of surfaces Casagrande, Cinzia Algebraic Geometry Let X be a smooth, complex Fano 4-fold, and rho(X) its Picard number. We show that if rho(X)>12, then X is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial elementary contractions f: X->Y such that the image S of the exceptional divisor is a surface, together with the author's previous work on Fano 4-folds. In particular, given f: X->Y as above, under suitable assumptions we show that S is a smooth del Pezzo surface with -K_S given by the restriction of -K_Y. |
| title | Fano 4-folds with $b_2>12$ are products of surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2301.11953 |