Automorphisms of Finite Order on Rational Surfaces

Automorphisms of Finite Order on Rational Surfaces

Ž . 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-canonica...

Automorphisms of Finite Order on Rational Surfaces ( with an Appendix

Prime Order Automorphisms of Riemann Surfaces

Recently there has been renewed interest in the mappingclass group of a compact surface of genus g ≥ 2 and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphism on some Riemann surface of genus g. Here we give the details of the proof that there is an adapted basis for any conformal automorphism of prime order on a surface of genus...

Symplectic Automorphisms of Prime Order on K3 Surfaces

We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice of the K3 surface). With the help of elliptic fibrations we determine the invariant sublattice and its per...

Automorphisms of Order Three on Numerical Godeaux Surfaces

We prove that a numerical Godeaux surface cannot have an automorphism of order three.