inoue surfaces
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2018 ◽  
Vol 197 (1) ◽  
pp. 97-106
Author(s):  
Yifan Chen ◽  
YongJoo Shin
Keyword(s):  

2016 ◽  
Vol 271 (11) ◽  
pp. 3162-3185 ◽  
Author(s):  
Shouwen Fang ◽  
Valentino Tosatti ◽  
Ben Weinkove ◽  
Tao Zheng
Keyword(s):  

2016 ◽  
Vol 223 (1) ◽  
pp. 66-86 ◽  
Author(s):  
YIFAN CHEN

Let$S$be a smooth minimal complex surface of general type with$p_{g}=0$and$K^{2}=7$. We prove that any involution on$S$is in the center of the automorphism group of$S$. As an application, we show that the automorphism group of an Inoue surface with$K^{2}=7$is isomorphic to$\mathbb{Z}_{2}^{2}$or$\mathbb{Z}_{2}\times \mathbb{Z}_{4}$. We construct a$2$-dimensional family of Inoue surfaces with automorphism groups isomorphic to$\mathbb{Z}_{2}\times \mathbb{Z}_{4}$.


2013 ◽  
Vol 149 (12) ◽  
pp. 2101-2138 ◽  
Author(s):  
Valentino Tosatti ◽  
Ben Weinkove

AbstractThe Chern–Ricci flow is an evolution equation of Hermitian metrics by their Chern–Ricci form, first introduced by Gill. Building on our previous work, we investigate this flow on complex surfaces. We establish new estimates in the case of finite time non-collapsing, analogous to some known results for the Kähler–Ricci flow. This provides evidence that the Chern–Ricci flow carries out blow-downs of exceptional curves on non-minimal surfaces. We also describe explicit solutions to the Chern–Ricci flow for various non-Kähler surfaces. On Hopf surfaces and Inoue surfaces these solutions, appropriately normalized, collapse to a circle in the sense of Gromov–Hausdorff. For non-Kähler properly elliptic surfaces, our explicit solutions collapse to a Riemann surface. Finally, we define a Mabuchi energy functional for complex surfaces with vanishing first Bott–Chern class and show that it decreases along the Chern–Ricci flow.


2013 ◽  
Vol 88 (4) ◽  
pp. 859-874 ◽  
Author(s):  
Marco Brunella
Keyword(s):  

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