Linear systems on blow-ups of Hirzebruch surfaces

2026/01/31 by Cyril J. Jacob, Ronnie Sebastian
#math.AG

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Abstract

Motivated by various equivalent versions of the SHGH conjecture for \mathbb P² 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.

Citations

• Seshadri constants and negative curves on blowups of ruled surfaces
• Rationality of Seshadri constants on blow-ups of ruled surfaces
• Seshadri constants on blow-ups of Hirzebruch surfaces
• Special homogeneous linear systems on Hirzebruch surfaces

Related

• Special homogeneous linear systems on Hirzebruch surfaces
• Seshadri constants on blow-ups of Hirzebruch surfaces
• Special homogeneous linear systems on Hirzebruch surfaces - algorithmic issues
• On the influence of the Segre Problem on the Mori cone of blown-up surfaces
• Equivalent conjectures on blowing-ups of \mathbb P²