For Hirzebruch surfaces, the algebraic exceptional set of a three-component normal-crossing curve with big K+B and no fiber or negative self-intersection component is finite and equals the hyper-bitangent set.
Hypertangency of plane curves and the algebraic ex- ceptional set.Proceedings of the London Mathematical Society, 130(6):e70063, 2025
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Algebraic Exceptional Set of a Three-Component Curve on Hirzebruch Surfaces
For Hirzebruch surfaces, the algebraic exceptional set of a three-component normal-crossing curve with big K+B and no fiber or negative self-intersection component is finite and equals the hyper-bitangent set.