Linear weighted bounded negativity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915120215490560 |
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| author | Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira |
| author_facet | Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira |
| contents | We propose a linear version of the weighted bounded negativity conjecture. It considers a smooth projective surface $X$ over an algebraically closed field of characteristic zero and predicts the existence of a common lower bound on $C^2/(D\cdot C)$ for all reduced and irreducible curves $C$ and all big and nef divisors such that $D\cdot C>0$, both on $X$.
We prove that, in the complex case, there exists such a bound for all nef divisors spanning a ray out an open covering of the limit rays of negative curves. In the same vein, we provide explicit bounds when $X$ is a rational surface.
Our proofs involve the existence of a foliation $\mathcal{F}$ on $X$ but most of our results are independent of $\mathcal{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear weighted bounded negativity Galindo, Carlos Monserrat, Francisco Pérez-Callejo, Elvira Algebraic Geometry 14C20, 14E15 We propose a linear version of the weighted bounded negativity conjecture. It considers a smooth projective surface $X$ over an algebraically closed field of characteristic zero and predicts the existence of a common lower bound on $C^2/(D\cdot C)$ for all reduced and irreducible curves $C$ and all big and nef divisors such that $D\cdot C>0$, both on $X$. We prove that, in the complex case, there exists such a bound for all nef divisors spanning a ray out an open covering of the limit rays of negative curves. In the same vein, we provide explicit bounds when $X$ is a rational surface. Our proofs involve the existence of a foliation $\mathcal{F}$ on $X$ but most of our results are independent of $\mathcal{F}$. |
| title | Linear weighted bounded negativity |
| topic | Algebraic Geometry 14C20, 14E15 |
| url | https://arxiv.org/abs/2501.14519 |