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On weighted bounded negativity for rational surfaces
- Publication Year :
- 2024
-
Abstract
- The weighted bounded negativity conjecture considers a smooth projective surface $X$ and looks for a common lower bound on the quotients $C^2/(D\cdot C)^2$, where $C$ runs over the integral curves on $X$ and $D$ over the big and nef divisors on $X$ such that $D \cdot C >0$. We focus our study on rational surfaces $Z$. Setting $\pi: Z \rightarrow Z_0$ a composition of blowups giving rise to $Z$, where $Z_0$ is the projective plane or a Hirzebruch surface, we give a common lower bound on $C^2/(H^* \cdot C)^2$ whenever $H^*$ is the pull-back of a nef divisor $H$ on $Z_0$. In addition, we prove that, only in the case when a nef divisor $D$ on $Z$ approaches the boundary of the nef cone, the quotients $C^2/(D\cdot C)^2$ could tend to minus infinity.<br />Comment: Comments are welcome
- Subjects :
- Mathematics - Algebraic Geometry
14C20, 14E15, 14J26
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.05466
- Document Type :
- Working Paper