On full exceptional collections of line bundles on del Pezzo surfaces

TL;DR

This paper proves that all maximal-length, numerically exceptional collections of line bundles on smooth del Pezzo surfaces are standard augmentations, hence they are exceptional and full, advancing the understanding of their structure.

Contribution

It establishes that such collections are standard augmentations, confirming their exceptionality and fullness, which was previously unknown.

Findings

All maximal-length, numerically exceptional line bundle collections are standard augmentations.

Such collections are proven to be exceptional.

These collections are full, covering the entire derived category.

Abstract

We prove that any numerically exceptional collection of maximal length, consisting of line bundles, on a smooth del Pezzo surface is a standard augmentation in the sense of L.Hille and M.Perling. We deduce that any such collection is exceptional and full.