Weighted Projective Lines as Fine Moduli Spaces of Quiver Representations

Abstract

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their canonical bundles, and show that they are rarely tilting. We also give a moduli construction for these total spaces for weighted projective lines with three orbifold points.

Key Words:

• Moduli space
• Quiver representation
• Weighted projective line

2010 Mathematics Subject Classification:

• 16G20
• 14D23

ACKNOWLEDGMENT

This work was initiated at Max Planck Institute for Mathematics, and completed at Korea Institute for Advanced Study. We thank both institutes for hospitality and nice research environment. We also thank the anonymous referee for suggesting a number of improvements.

Notes

Communicated by G. Leuschke.

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lagb.