A result on the generic Picard number of surfaces in fake weighted projective 3-spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918534875971584 |
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| author | Giesler, Julius |
| author_facet | Giesler, Julius |
| contents | We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge), keeping track of the geometric genus, and using vanishing cohomology classes to construct a rational Picard class on the surface not proportional to the canonical divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A result on the generic Picard number of surfaces in fake weighted projective 3-spaces Giesler, Julius Algebraic Geometry We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge), keeping track of the geometric genus, and using vanishing cohomology classes to construct a rational Picard class on the surface not proportional to the canonical divisor. |
| title | A result on the generic Picard number of surfaces in fake weighted projective 3-spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.25709 |