Rationality of Seshadri constants on blow-ups of ruled surfaces

2024/07/26 by Hanumanthu, Krishna, Jacob, Cyril J., N., Suhas B. +1 · 1 citation
#14C20 #14E05 #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.18678

Abstract

In this note, we continue the study of Seshadri constants on blow-ups of Hirzebruch surfaces initiated in arXiv:2312.14555. Now we consider blow-ups of ruled surfaces more generally. We propose a conjecture for classifying all the negative self-intersection curves on the blow-up of a ruled surface at very general points, analogous to the (-1)-curves conjecture in ℙ². Assuming this conjecture is true, we exhibit an ample line bundle with an irrational Seshadri constant at a very general point on such a surface.

Cited by

• Linear systems on blow-ups of Hirzebruch surfaces

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