Linear systems on rational surfaces

Cyril J. Jacob; Ronnie Sebastian

Linear systems on rational surfaces

Algebraic Geometry 2026-01-30 v1

Authors: Cyril J. Jacob , Ronnie Sebastian

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 $r\leqslant e+4$ very general points.

Keywords

blow-up conjectures and proofs

Cite

@article{arxiv.2601.21958,
  title  = {Linear systems on rational surfaces},
  author = {Cyril J. Jacob and Ronnie Sebastian},
  journal= {arXiv preprint arXiv:2601.21958},
  year   = {2026}
}

Comments

9 pages, Comments are welcome

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