SYMPLECTIC RATIONAL G-SURFACES AND EQUIVARIANT SYMPLECTIC CONES

We give characterizations of a finite group G acting symplectically on a rational surface (CP2 blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of G-conic bundles versus G-del Pezzo surfaces for the corresponding G-rational surfaces, analogous to a classical result in algebraic geometry. Besides the characterizations of the group G (which is completely determined for the case of CP2 #N (CP2) over bar, N = 2, 3, 4), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given G-rational surface.