Linear systems on blow-ups of Hirzebruch surfaces

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Cyril J. Jacob, Ronnie Sebastian
DOI: 10.48550/arxiv.2601.21958
Cited by: 0

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.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Commutative Algebra and Its Applications Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
29 January 2026
Document type
Preprint