Polarized cylinders on blow-ups of weighted projective planes

TL;DR

This paper investigates polarized cylinders on specific rational surfaces derived from blow-ups of weighted projective planes, focusing on surfaces obtained by blowing up points on $ ext{P}(1,1,m)$ and their geometric properties.

Contribution

It introduces a detailed study of polarized cylinders on these rational surfaces, expanding understanding of their structure and occurrence in weighted hypersurfaces.

Findings

Identification of conditions for polarized cylinders on these surfaces

Connection between blow-up configurations and cylinder existence

Insights into the geometry of weighted hypersurfaces

Abstract

We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane $\mathbb{P}(1,1,m)$. These surfaces appear naturally as weighted hypersurfaces or quasi-smooth complete intersections.