NOTES ON AUTOMORPHISMS OF SURFACES OF GENERAL TYPE WITH AND

2016 ◽  
Vol 223 (1) ◽  
pp. 66-86 ◽  
Author(s):  
YIFAN CHEN
Keyword(s):  
Automorphism Group ◽  
General Type ◽  
Automorphism Groups ◽  
Complex Surface ◽  
Surfaces Of General Type ◽  
Surface Of General Type ◽  
Inoue Surfaces

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$\mathbb{Z}_{2}\times \mathbb{Z}_{4}$.

scholarly journals CANONICALLY FIBERED SURFACES OF GENERAL TYPE

2018 ◽  
Vol 19 (1) ◽  
pp. 209-229
Author(s):  
Xin Lü
Keyword(s):  
General Type ◽  
Complex Surface ◽  
The Other ◽  
Complex Surfaces ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Canonical Map ◽  
Other Hand ◽  
Surface Of General Type

In this paper, we construct the first examples of complex surfaces of general type with arbitrarily large geometric genus whose canonical maps induce non-hyperelliptic fibrations of genus $g=4$, and on the other hand, we prove that there is no complex surface of general type whose canonical map induces a hyperelliptic fibrations of genus $g\geqslant 4$ if the geometric genus is large.

A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves

2016 ◽  
Vol 68 (1) ◽  
pp. 67-87
Author(s):  
Hirotaka Ishida
Keyword(s):  
Lower Bound ◽  
General Type ◽  
Hyperelliptic Curves ◽  
Surfaces Of General Type ◽  
Linear Pencil ◽  
Surface Of General Type

AbstractLet S be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration whose slope is less than or equal to four, we give a lower bound on the Euler–Poincaré characteristic of S. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.

On Abelian automorphism groups of fibred surfaces of small genus

2001 ◽  
Vol 130 (1) ◽  
pp. 161-174 ◽  
Author(s):  
JIN-XING CAI
Keyword(s):  
Automorphism Group ◽  
General Type ◽  
Automorphism Groups ◽  
Projective Surface ◽  
Canonical Divisor ◽  
Smooth Projective Surface ◽  
Small Genus

It is proved that, for a complex minimal smooth projective surface S of general type with a pencil of genus g = 3 or 4, any Abelian automorphism group of S is of order [les ] 12K2S + 96(g − 1), provided K2S > 8(g − 1)2, where KS is the canonical divisor of S.

scholarly journals THE BICANONICAL MAP OF SURFACES WITH pg = 0 AND K2 [ges ] 7

2001 ◽  
Vol 33 (3) ◽  
pp. 265-274 ◽  
Author(s):  
MARGARIDA MENDES LOPES ◽  
RITA PARDINI
Keyword(s):  
Minimal Surface ◽  
General Type ◽  
Surfaces Of General Type ◽  
Bicanonical Map ◽  
Surface Of General Type

A minimal surface of general type with pg(S) = 0 satisfies 1 [les ] K2 [les ] 9, and it is known that the image of the bicanonical map φ is a surface for K2S [ges ] 2, whilst for K2S [ges ] 5, the bicanonical map is always a morphism. In this paper it is shown that φ is birational if K2S = 9, and that the degree of φ is at most 2 if K2S = 7 or K2S = 8.By presenting two examples of surfaces S with K2S = 7 and 8 and bicanonical map of degree 2, it is also shown that this result is sharp. The example with K2S = 8 is, to our knowledge, a new example of a surface of general type with pg = 0.The degree of φ is also calculated for two other known surfaces of general type with pg = 0 and K2S = 8. In both cases, the bicanonical map turns out to be birational.

scholarly journals Automorphisms of surfaces of general type with acting trivially in cohomology

2013 ◽  
Vol 149 (10) ◽  
pp. 1667-1684 ◽  
Author(s):  
Jin-Xing Cai ◽  
Wenfei Liu ◽  
Lei Zhang
Keyword(s):  
Automorphism Group ◽  
Minimal Surfaces ◽  
General Type ◽  
Cohomology Ring ◽  
Complete Classification ◽  
Surfaces Of General Type

AbstractIn this paper we prove that surfaces of general type with irregularity $q\geq 3$ are rationally cohomologically rigidified, and so are minimal surfaces $S$ with $q(S)= 2$ unless ${ K}_{S}^{2} = 8\chi ({ \mathcal{O} }_{S} )$. Here a surface $S$ is said to be rationally cohomologically rigidified if its automorphism group $\mathrm{Aut} (S)$ acts faithfully on the cohomology ring ${H}^{\ast } (S, \mathbb{Q} )$. As examples we give a complete classification of surfaces isogenous to a product with $q(S)= 2$ that are not rationally cohomologically rigidified.

Classification of surfaces of general type with Euler number 3

2013 ◽  
Vol 2013 (679) ◽  
pp. 1-22 ◽  
Author(s):  
Sai-Kee Yeung
Keyword(s):  
Projective Plane ◽  
Recent Work ◽  
Present Article ◽  
Smooth Surface ◽  
General Type ◽  
Euler Number ◽  
Projective Planes ◽  
Surfaces Of General Type ◽  
Surface Of General Type

Abstract The smallest topological Euler–Poincaré characteristic supported on a smooth surface of general type is 3. In this paper, we show that such a surface has to be a fake projective plane unless h1, 0(M) = 1. Together with the classification of fake projective planes given by Prasad and Yeung, the recent work of Cartwright and Steger, and a proof of the arithmeticity of the lattices involved in the present article, this gives a classification of such surfaces.

Sign in / Sign up

Export Citation Format

Share Document