scholarly journals Surfaces of general type with q = 2 are rigidified

2018 ◽  
Vol 20 (07) ◽  
pp. 1750084 ◽  
Author(s):  
Wenfei Liu
Keyword(s):  
General Type ◽  
Geometric Characterization ◽  
Projective Surface ◽  
Holomorphic Automorphism ◽  
Surfaces Of General Type ◽  
Nontrivial Automorphism ◽  
Smooth Projective Surface ◽  
Surface Of General Type

Let [Formula: see text] be a minimal smooth projective surface of general type with irregularity [Formula: see text]. We show that, if [Formula: see text] has a nontrivial holomorphic automorphism acting trivially on the cohomology with rational coefficients, then it is a surface isogenous to a product. As a consequence of this geometric characterization, one infers that no nontrivial automorphism of surfaces of general type with [Formula: see text] (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.

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.

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.

Irregularity of canonical pencils for a threefold of general type

1999 ◽  
Vol 125 (1) ◽  
pp. 83-87 ◽  
Author(s):  
MENG CHEN ◽  
ZHIJIE J. CHEN
Keyword(s):  
General Type ◽  
Canonical System ◽  
Projective Surface ◽  
Base Points ◽  
Surface Of General Type

Let X be a complex nonsingular projective threefold of general type. Suppose the canonical system of X is composed of a pencil, i.e. dimΦ∼KX∼(X)=1. It is often important to understand birational invariants of X such as pg(X), q(X), h2(OX) and χ(OX) etc. In this paper, we mainly study the irregularity of X.We may suppose that ∼KX∼ is free of base points. There is a natural fibration f[ratio ]X→C onto a nonsingular curve after the Stein factorization of Φ∼KX∼. Let F be a general fibre of f, then we know that F is a nonsingular projective surface of general type. Set b[ratio ]=g(C) and pg(F), q(F) for the respective invariants of F. The main result is the following theorem.

scholarly journals MIXED QUASI-ÉTALE QUOTIENTS WITH ARBITRARY SINGULARITIES

2014 ◽  
Vol 57 (1) ◽  
pp. 143-165 ◽  
Author(s):  
DAVIDE FRAPPORTI ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Minimal Surface ◽  
Finite Subset ◽  
General Type ◽  
Minimal Resolution ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Canonical Class ◽  
Two Factors ◽  
Surface Of General Type ◽  
Étale Quotients

AbstractA mixed quasi-étale quotient is the quotient of the product of a curve of genus at least 2 with itself by the action of a group which exchanges the two factors and acts freely outside a finite subset. A mixed quasi-étale surface is the minimal resolution of its singularities. We produce an algorithm computing all mixed quasi-étale surfaces with given geometric genus, irregularity and self-intersection of the canonical class. We prove that all irregular mixed quasi-étale surfaces of general type are minimal. As an application, we classify all irregular mixed quasi-étale surfaces of general type with genus equal to the irregularity, and all the regular ones with K2 > 0, thus constructing new examples of surfaces of general type with χ = 1. We mention the first example of a minimal surface of general type with pg = q = 1 and Albanese fibre of genus bigger than K2.

scholarly journals Some infinite sequences of canonical covers of degree 2

2021 ◽  
Vol 21 (1) ◽  
pp. 143-148
Author(s):  
Nguyen Bin
Keyword(s):  
General Type ◽  
Canonical System ◽  
Surfaces Of General Type ◽  
Canonical Map ◽  
Base Points ◽  
Surface Of General Type ◽  
Infinite Sequences

Abstract In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

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.

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 Even canonical surfaces with small K2, III

1996 ◽  
Vol 143 ◽  
pp. 1-11 ◽  
Author(s):  
Kazuhiro Konno
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Canonical Divisor ◽  
Surface Of General Type ◽  
Present Part ◽  
Albanese Map ◽  
First Main Theorem

This is a continuation of [5]. In the present part, we study irregular even surfaces of general type with K < 4χ, where K and χ denote respectively a canonical divisor and the holomorphic Euler-Poincaré characteristic. As the first main theorem, we show the following: THEOREM 1. For any irregular even surface of general type with K < 4χ, the image of the Albanese map is a curve.

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