A Note on the Canonical Divisor of Quasi-homogeneous Affine Algebraic Varieties

Abstract

We give a necessary and sufficient condition for the canonical divisor to vanish on a quasi-homogeneous affine algebraic variety.

Key Words:

• Quasi-homogeneous spaces
• Vector bundles

2010 Mathematics Subject Classification:

• Primary: 14J60
• 14M17
• Secondary: 20C15

ACKNOWLEDGMENTS

I wish to thank Dmitriy Rumynin for his valuable suggestions to prove the main result. This work was mainly carried out during my Ph.D. studies at the University of Warwick under the supervision of Miles Reid, to whom I would like to express my deepest gratitude. I acknowledge useful scientific discussions with Stavros Papadakis and Stephen Coughlan.