Logarithmic vector bundles on the blown-up surface

TL;DR

This paper investigates the properties of logarithmic vector bundles on blown-up surfaces, focusing on their ability to uniquely determine the arrangements of curves, and explores their Torelli-type reconstruction capabilities.

Contribution

It introduces a study of logarithmic vector bundles on blown-up surfaces and examines their Torelli properties for certain curve arrangements.

Findings

Logarithmic vector bundles can sometimes be recovered from arrangements.

Certain arrangements are Torelli arrangements, allowing reconstruction from bundles.

The study advances understanding of vector bundle and curve arrangement relationships.

Abstract

We study the logarithmic vector bundles associated to arrangements of smooth irreducible curves with small degree on the blow-up of the projective plane at one point. We then investigate whether they are Torelli arrangements, that is, they can be recovered from the attached logarithmic vector bundles.