Algebraic exceptional set of a three-component curve on Hirzebruch surfaces
Abstract
Abstract We study the algebraic exceptional set of a three-component curve $B$ with normal crossings on a Hirzebruch surface $\mathbb{F}_{e}$. If $K_{\mathbb{F}_{e}}+B$ is big and no component of $B$ is a fiber or the rational curve with negative self-intersection, we prove that the algebraic exceptional set is finite and, in most cases, give it an effective bound. We also prove that the algebraic exceptional set coincides with the set of curves that are hyper-bitangent to $B$.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 11
- Publication date
- 22 May 2026
- Language
- EN