On the order of the automorphism group of a surface of general type

1990 ◽  
Vol 205 (1) ◽  
pp. 321-329 ◽  
Author(s):  
A. T. Huckleberry ◽  
M. Sauer
Keyword(s):  
Automorphism Group ◽  
General Type ◽  
Surface Of General Type

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

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.

scholarly journals A simply connected surface of general type withpg= 0 andK2= 4

2009 ◽  
Vol 13 (3) ◽  
pp. 1483-1494 ◽  
Author(s):  
Heesang Park ◽  
Jongil Park ◽  
Dongsoo Shin
Keyword(s):  
General Type ◽  
Connected Surface ◽  
Surface Of General Type ◽  
Simply Connected

Degenerate surfaces in higher space

1933 ◽  
Vol 29 (1) ◽  
pp. 88-94 ◽  
Author(s):  
L. Roth
Keyword(s):  
General Type ◽  
General Character ◽  
Space Curves ◽  
Single Curve ◽  
General Surface ◽  
Previous Note ◽  
Surface Of General Type ◽  
Degenerate Curve

1. In a previous note the author has examined the systems of tangent planes to a degenerate surface in S3 consisting of n planes, regarded as the limit of a general surface of the same order. It is well known that a pair of space curves which are the limiting form of a non-degenerate curve must have a certain number of intersections; hence, if a surface in higher space degenerates into a number of surfaces, these must intersect in curves of various orders. In the present paper we consider the nature of the envelope to a surface consisting of two general surfaces of S4 having in common a single curve of general character, the degenerate surface being regarded as the limit of some surface of general type. The same conclusions hold for a similar degenerate surface in Sr (r>4).

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 Geometry of the Wiman–Edge monodromy

2021 ◽  
pp. 1-29
Author(s):  
Matthew Stover
Keyword(s):  
Automorphism Group ◽  
Modular Group ◽  
Alternating Group ◽  
Projective Surface ◽  
Congruence Condition ◽  
Symmetric Manifold ◽  
New Information ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Surface Of General Type

The Wiman–Edge pencil is a pencil of genus 6 curves for which the generic member has automorphism group the alternating group [Formula: see text]. There is a unique smooth member, the Wiman sextic, with automorphism group the symmetric group [Formula: see text]. Farb and Looijenga proved that the monodromy of the Wiman–Edge pencil is commensurable with the Hilbert modular group [Formula: see text]. In this note, we give a complete description of the monodromy by congruence conditions modulo 4 and 5. The congruence condition modulo 4 is new, and this answers a question of Farb–Looijenga. We also show that the smooth resolution of the Baily–Borel compactification of the locally symmetric manifold associated with the monodromy is a projective surface of general type. Lastly, we give new information about the image of the period map for the pencil.

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