CANONICALLY FIBERED SURFACES 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.

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Cuspidal quintics and surfaces with , and 5-torsion

LMS Journal of Computation and Mathematics ◽

10.1112/s1461157015000315 ◽

2016 ◽

Vol 19 (1) ◽

pp. 42-53

Author(s):

Carlos Rito

Keyword(s):

Computer Algebra ◽

General Type ◽

Free Action ◽

The Other ◽

Singular Set ◽

Canonical Map ◽

Singular Sets ◽

Surface Of General Type ◽

Quintic Threefold ◽

Hyperplane Sections

If $S$ is a quintic surface in $\mathbb{P}^{3}$ with singular set 15 3-divisible ordinary cusps, then there is a Galois triple cover ${\it\phi}:X\rightarrow S$ branched only at the cusps such that $p_{g}(X)=4$, $q(X)=0$, $K_{X}^{2}=15$ and ${\it\phi}$ is the canonical map of $X$. We use computer algebra to search for such quintics having a free action of $\mathbb{Z}_{5}$, so that $X/\mathbb{Z}_{5}$ is a smooth minimal surface of general type with $p_{g}=0$ and $K^{2}=3$. We find two different quintics, one of which is the van der Geer–Zagier quintic; the other is new.We also construct a quintic threefold passing through the 15 singular lines of the Igusa quartic, with 15 cuspidal lines there. By taking tangent hyperplane sections, we compute quintic surfaces with singular sets $17\mathsf{A}_{2}$, $16\mathsf{A}_{2}$, $15\mathsf{A}_{2}+\mathsf{A}_{3}$ and $15\mathsf{A}_{2}+\mathsf{D}_{4}$.

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MIXED QUASI-ÉTALE QUOTIENTS WITH ARBITRARY SINGULARITIES

Glasgow Mathematical Journal ◽

10.1017/s0017089514000184 ◽

2014 ◽

Vol 57 (1) ◽

pp. 143-165 ◽

Cited By ~ 6

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.

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Some infinite sequences of canonical covers of degree 2

Advances in Geometry ◽

10.1515/advgeom-2020-0028 ◽

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.

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NOTES ON AUTOMORPHISMS OF SURFACES OF GENERAL TYPE WITH AND

Nagoya Mathematical Journal ◽

10.1017/nmj.2016.24 ◽

2016 ◽

Vol 223 (1) ◽

pp. 66-86 ◽

Cited By ~ 1

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

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

Canadian Journal of Mathematics ◽

10.4153/cjm-2015-032-8 ◽

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.

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

Communications in Contemporary Mathematics ◽

10.1142/s0219199713500107 ◽

2014 ◽

Vol 16 (02) ◽

pp. 1350010 ◽

Cited By ~ 5

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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ℤ3-actions on Horikawa surfaces

International Journal of Mathematics ◽

10.1142/s0129167x2150097x ◽

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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Notes on the Genus Rhipicephalus, with the Description of New Species, and the Consideration of some Species hitherto described

Parasitology ◽

10.1017/s0031182000000032 ◽

1912 ◽

Vol 5 (1) ◽

pp. 1-20 ◽

Cited By ~ 11

Author(s):

Cecil Warburton

Keyword(s):

New Species ◽

General Type ◽

The Other ◽

Single Individual ◽

Other Hand ◽

Identification Of Species ◽

The One ◽

Range Of Variation ◽

A New Species

The identification of species of Rhipicephalus is likely to give more trouble than is the case with any other genus of Ixodidae, for while, on the one hand, there are few species which depart greatly from the general type, on the other hand the range of variation within the species is extremely great. In no genus is it so dangerous to describe a new species from a single individual, especially if the specimen be a female.

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