Automorphisms of Finite Order on Rational Surfaces

2000/09/13 by D. Q. Zhang, D. -Q. Zhang, Zhang, D. -Q.
Mathematics · #14J26 #14J50 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14J26 #msc:14J50

paper · pdf · doi:10.48550/arxiv.math/0009126

with an Appendix by I. Dolgachev; to appear in Journal of Algebra

arxiv created 2000/09/13 · openalex publication_date 2000/09/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify minimal pairs (X, G) for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X^G and the quotient surface Y = X/G as well as the fundamental group of the smooth part of Y. The realization of each pair is included. Mori's extremal ray theory and recent results of Alexeev and also Ambro on the existence of good anti-canonical divisors are used.

Related

• The automorphism group of a rational projective k*-surface
• Automorphisms of finite order on Gorenstein del Pezzo surfaces
• Automorphisms of Minimal Surfaces of General Type with K_S² = 1, p_g = 2
• Rational surfaces with a large group of automorphisms
• Rational surfaces with a non-arithmetic automorphism group