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October 2021 Symplectic rational $G$-surfaces and equivariant symplectic cones
Weimin Chen, Tian-Jun Li, Weiwei Wu
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J. Differential Geom. 119(2): 221-260 (October 2021). DOI: 10.4310/jdg/1632506334

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.

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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

Information

Received: 24 August 2017; Accepted: 27 January 2020; Published: October 2021
First available in Project Euclid: 27 September 2021

Digital Object Identifier: 10.4310/jdg/1632506334

Subjects:
Primary: 14E07, 57R17, 57S17

Rights: Copyright © 2021 Lehigh University

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Vol.119 • No. 2 • October 2021
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