Abstract
We give characterizations of a finite group $G$ acting symplectically on a rational surface ($\mathbb{CP}^2$ 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 $\mathbb{CP}^2 \# N \overline{\mathbb{CP}^2}, N={2,3,4}$), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given $G$-rational surface.
Citation
Weimin Chen. Tian-Jun Li. Weiwei Wu. "Symplectic rational $G$-surfaces and equivariant symplectic cones." J. Differential Geom. 119 (2) 221 - 260, October 2021. https://doi.org/10.4310/jdg/1632506334
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