scholarly journals On the structure of minimal surfaces of general type with $2p_g=(K^2)+2$

1978 ◽  
Vol 18 (1) ◽  
pp. 137-171 ◽  
Author(s):  
Masayoshi Miyanishi ◽  
Kiyotaka Nakamura
Keyword(s):  
Minimal Surfaces ◽  
General Type ◽  
Surfaces Of General Type

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.

scholarly journals Surfaces with pg = q = 2, K2 = 6, and Albanese Map of Degree 2

2013 ◽  
Vol 65 (1) ◽  
pp. 195-221 ◽  
Author(s):  
Matteo Penegini ◽  
Francesco Polizzi
Keyword(s):  
Moduli Space ◽  
Minimal Surfaces ◽  
General Type ◽  
Disjoint Union ◽  
Double Cover ◽  
Surfaces Of General Type ◽  
Irreducible Components ◽  
Albanese Map

AbstractWe classify minimal surfaces of general type with pg = q = 2 and K2 = 6 whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components MIa, MIb, MII of dimension 4, 4, 3, respectively.

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 NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES

2014 ◽  
Vol 16 (02) ◽  
pp. 1350010 ◽  
Author(s):  
GILBERTO BINI ◽  
FILIPPO F. FAVALE ◽  
JORGE NEVES ◽  
ROBERTO PIGNATELLI
Keyword(s):  
Fundamental Group ◽  
Moduli Space ◽  
General Type ◽  
Picard Number ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Genus Zero ◽  
New Family ◽  
Hodge Numbers ◽  
Projective Lines

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

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