scholarly journals Deformations and local torelli theorem for certain surfaces of general type

1979 ◽  
pp. 605-629 ◽  
Author(s):  
Sampei Usui
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Torelli Theorem

Infinitesimal Torelli theorem for surfaces of general type with certain invariants

2005 ◽  
Vol 118 (2) ◽  
pp. 151-160
Author(s):  
Masaaki Murakami
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Torelli Theorem

On the Infinitesimal Torelli theorem for certain irregular surfaces of general type

1988 ◽  
Vol 280 (2) ◽  
pp. 285-302 ◽  
Author(s):  
Igor Reider
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Irregular Surfaces ◽  
Torelli Theorem

scholarly journals On Surfaces of General Type withpg = q = 1 Isogenous to a Product of Curves

2008 ◽  
Vol 36 (6) ◽  
pp. 2023-2053 ◽  
Author(s):  
Francesco Polizzi
Keyword(s):  
General Type ◽  
Surfaces Of General Type

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.

scholarly journals Surfaces of general type with $p_g=1$ and $(K,\,K)=1$. I

1980 ◽  
Vol 13 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Andrei N. Todorov
Keyword(s):  
General Type ◽  
Surfaces Of General Type

ℤ3-actions on Horikawa surfaces

2021 ◽  
pp. 2150097
Author(s):  
Vicente Lorenzo
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Admissible Pair ◽  
Algebraic Surfaces ◽  
The Other ◽  
Connected Components ◽  
Surfaces Of General Type ◽  
Canonical Models ◽  
Normal Surfaces ◽  
Stable Surfaces

Minimal algebraic surfaces of general type [Formula: see text] such that [Formula: see text] are called Horikawa surfaces. In this note, [Formula: see text]-actions on Horikawa surfaces are studied. The main result states that given an admissible pair [Formula: see text] such that [Formula: see text], all the connected components of Gieseker’s moduli space [Formula: see text] contain surfaces admitting a [Formula: see text]-action. On the other hand, the examples considered allow us to produce normal stable surfaces that do not admit a [Formula: see text]-Gorenstein smoothing. This is illustrated by constructing non-smoothable normal surfaces in the KSBA-compactification [Formula: see text] of Gieseker’s moduli space [Formula: see text] for every admissible pair [Formula: see text] such that [Formula: see text]. Furthermore, the surfaces constructed belong to connected components of [Formula: see text] without canonical models.

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