scholarly journals Cuspidal quintics and surfaces with , and 5-torsion

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 $15\mathsf{A}_{2}+\mathsf{D}_{4}$.

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.

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 Beauville Surfaces with Abelian Beauville Group

2014 ◽  
Vol 114 (2) ◽  
pp. 191 ◽  
Author(s):  
G. González-Diez ◽  
G. A. Jones ◽  
D. Torres-Teigell
Keyword(s):  
General Type ◽  
Automorphism Groups ◽  
Free Action ◽  
Rigid Surface ◽  
Isomorphism Classes ◽  
Surface Of General Type ◽  
Beauville Surfaces ◽  
A Finite Group ◽  
Beauville Group ◽  
Beauville Surface

A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves $C_{1}$, $C_{2}$ of genera $g_{1},g_{2}\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\cong \mathsf{Z}_{n}^{2}$ with $\gcd(n,6)=1$ by a result of Catanese). For each such $n$ we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined over $\mathsf{Q}$.

Persona y libertad: lecturas desde la diversidad, la complejidad y la conflictividad

2020 ◽  
Author(s):  
Víctor Martin-Fiorino ◽  
Ignacio Miralbell ◽  
Eduardo Molina ◽  
Luis Mariano de la Maza ◽  
María Belén Tell ◽  
...  
Keyword(s):  
Free Action ◽  
The Other ◽  
Personal Dignity ◽  
The Will ◽  
Anthropological Approach ◽  
Community Environments

This book analyzes, from diverse but convergent historical and theoretical visions, the central problems of the anthropological structure of the person in relation to freedom - as the center of personal dignity - and with the possibilities and limits of free action and its conditionings. The text highlights the tension between rationality and responsibility when studying freedom from different perspectives, and as a decision of the person who responsibly practice it to the other people, from the will, experience and intersubjectivity. By the hands of authors, from Aristotle to contemporary anthropology, who are essential references, the text clarifies the origin of the choices in which freedom is expressed and allows deepening its understanding as an idea and as a content, from the complexity and conflict. The work studies fundamental aspects of the person-freedom relationship from ethics, psychology, politics, metaphysics and theology, and highlights the value of purpose, autonomy and community environments in which freedom is realized, keeping in mind an integrative anthropological approach. Finally, the argument about the centrality of the person is especially valuable in times of visions that minimize the human to consumption, production or ideology. The conclusions of this volume revalue the foundation and the possibility of free action that makes the being human responsible and committed.

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.

Fielding and Richardson

PMLA ◽  
1966 ◽  
Vol 81 (5) ◽  
pp. 381-388
Author(s):  
William Park
Keyword(s):  
Twentieth Century ◽  
Eighteenth Century ◽  
Human Nature ◽  
General Type ◽  
Common Ground ◽  
The Other ◽  
The Novel ◽  
Tom Jones ◽  
The Common ◽  
The One

But the Discovery [of when to laugh and when to cry] was reserved for this Age, and there are two Authors now living in this Metropolis, who have found out the Art, and both brother Biographers, the one of Tom Jones, and the other of Clarissa.author of Charlotte SummersRather than discuss the differences which separate Fielding and Richardson, I propose to survey the common ground which they share with each other and with other novelists of the 1740's and 50's. In other words I am suggesting that these two masters, their contemporaries, and followers have made use of the same materials and that as a result the English novels of the mid-eighteenth century may be regarded as a distinct historic version of a general type of literature. Most readers, it seems to me, do not make this distinction. They either think that the novel is always the same, or they believe that one particular group of novels, such as those written in the early twentieth century, is the form itself. In my opinion, however, we should think of the novel as we do of the drama. No one kind of drama, such as Elizabethan comedy or Restoration comedy, is the drama itself; instead, each is a particular manifestation of the general type. Each kind bears some relationship to the others, but at the same time each has its own identity, which we usually call its conventions. By conventions I mean not only stock characters, situations, and themes, but also notions and assumptions about the novel, human nature, society, and the cosmos itself. If we compare one kind of novel to another without first considering the conventions of each, we are likely to make the same mistake that Thomas Rymer did when he blamed Shakespeare for not conforming to the canons of classical French drama.

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.

scholarly journals Modifications and Cobounding Manifolds

1960 ◽  
Vol 12 ◽  
pp. 503-528 ◽  
Author(s):  
Andrew H. Wallace
Keyword(s):  
Algebraic Variety ◽  
Finite Sequence ◽  
Differentiable Manifold ◽  
The Other ◽  
Algebraic Varieties ◽  
The Given ◽  
Hyperplane Sections

The object of this paper is to establish a simple connection between Thorn's theory of cobounding manifolds and the theory of modifications. The former theory is given in detail in (8) and sketched in (3), while the latter is worked out in (1). In particular in (1) it is shown that the only modifications which can transform one differentiable manifold into another are what I call below spherical modifications, which consist in taking out a sphere from the given manifold and replacing it by another. The main result is that manifolds cobound if and only if each is obtainable from the other by a finite sequence of spherical modifications.The technique consists in approximating the manifolds by pieces of algebraic varieties. Thus if M1 and M2 form the boundary of M, the last is taken to be part of an algebraic variety such that M1 and M2 are two members of a pencil of hyperplane sections.

Reinforcement of Polymers. I. Tear Resistance of Filled Mixes and Adhesion of Elastomer to Filler as a Function of Duration and Temperature of Elastomer and Filler Contact

1968 ◽  
Vol 41 (3) ◽  
pp. 601-607
Author(s):  
V. G. Raevskii ◽  
S. M. Yagnyatinskaya ◽  
S. N. Episeeva ◽  
S. S. Voyutskii
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Surface Crack ◽  
General Type ◽  
Physicomechanical Properties ◽  
The Other ◽  
Local Defect ◽  
System Components ◽  
Selection Of ◽  
Tear Resistance

Abstract In accordance with the concepts being developed by the authors of the present paper, the influence of fillers on the properties of filled systems is determined by adhesion of the polymer to the filler. There are indications of the significance of this factor in many papers dealing with the study of reinforcement. However, they do not advance adhesion as a basic factor which determines reinforcement. This has become possible after the development of a procedure for the evaluation of adhesion of polymers to powdered fillers. This paper lists experimental data on the correlation between the duration and temperature of contact of the elastomer with filler particles on the tear resistance of filled mixes, on one hand, and the time and temperature dependence of the adhesion of the system components to one another, on the other. The selection of tear resistance as a characteristic of the physicomechanical properties of the system is governed by the fact that failure starts, as a rule, from a random local defect. Most frequently this is a small cut or surface crack. For this reason, the assertion of a number of researchers that the operating properties of products are more fully characterized by tear resistance rather than by tensile strength is fully acceptable. Besides, tearing is the most general type of destruction of materials, inasmuch as it takes place during rupture as well as during wear.

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