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arXiv · 1708.07500

Symplectic rational $G$-surfaces and equivariant symplectic cones

Weimin Chen·Tian-Jun Li·Weiwei Wu
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Abstract

We give characterizations of a finite group $G$ acting symplectically on a rational surface ($\mathbb{C}P^2$ 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 $\mathbb{C}P^2\# N\overline{\mathbb{C}P^2}$, $N=2,3,4$), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given $G$-rational surface.

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Weimin Chen, Tian-Jun Li, Weiwei Wu. 2017-08-24. Symplectic rational $G$-surfaces and equivariant symplectic cones. https://arxiv.org/abs/1708.07500

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