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arXiv · 2601.21958

Linear systems on blow-ups of Hirzebruch surfaces

Cyril J. Jacob·Ronnie Sebastian
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Abstract

Motivated by various equivalent versions of the SHGH conjecture for $\mathbb P^2$ blown up at very general points, we propose a similar conjecture for Hirzebruch surfaces. We prove that this conjecture is true for the Hirzebruch surface $\mathbb F_e$ blown up at $r\leqslant e+5$ very general points.

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Cyril J. Jacob, Ronnie Sebastian. 2026-01-29. Linear systems on blow-ups of Hirzebruch surfaces. https://arxiv.org/abs/2601.21958

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