scholarly journals The basepoint-freeness threshold of a very general abelian surface

2022 ◽  
Vol 28 (2) ◽  
Author(s):  
Andrés Rojas
Keyword(s):  
Main Tool ◽  
Abelian Surface ◽  
Ideal Sheaf ◽  
Abelian Surfaces ◽  
New Information ◽  
In Virtue Of ◽  
The Ideal ◽  
Rank Functions

AbstractFor abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.

scholarly journals Degenerations of the generic square matrix, the polar map and the determinantal structure

2018 ◽  
Vol 28 (07) ◽  
pp. 1255-1297 ◽  
Author(s):  
Rainelly Cunha ◽  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Hessian Matrix ◽  
Main Tool ◽  
Affirmative Answer ◽  
Ideal Theory ◽  
Geometric Means ◽  
The Matrix ◽  
Hessian Determinant ◽  
The Ideal ◽  
Polar Map ◽  
Square Matrix

One studies certain degenerations of the generic square matrix over a field [Formula: see text] along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. The main tool comes from commutative algebra, with emphasis on ideal theory and syzygy theory. The structure of the polar map is completely identified and the main properties of the ideal of submaximal minors are determined. Cases where the degenerated determinant has non-vanishing Hessian determinant show that the former is a factor of the latter with the (Segre) expected multiplicity, a problem envisaged by Landsberg–Manivel–Ressayre by geometric means. Another byproduct is an affirmative answer to a question of F. Russo concerning the codimension in the polar image of the dual variety to a hypersurface.

scholarly journals ALBANESE VARIETIES OF CYCLIC COVERS OF THE PROJECTIVE PLANE AND ORBIFOLD PENCILS

2016 ◽  
Vol 227 ◽  
pp. 189-213
Author(s):  
E. ARTAL BARTOLO ◽  
J. I. COGOLLUDO-AGUSTÍN ◽  
A. LIBGOBER
Keyword(s):  
Projective Plane ◽  
Fundamental Group ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Plane Curves ◽  
Abelian Surface ◽  
Singular Curve ◽  
Cyclic Covers ◽  
Genus 2 ◽  
Multiple Fibers

The paper studies a relation between fundamental group of the complement to a plane singular curve and the orbifold pencils containing it. The main tool is the use of Albanese varieties of cyclic covers ramified along such curves. Our results give sufficient conditions for a plane singular curve to belong to an orbifold pencil, that is, a pencil of plane curves with multiple fibers inducing a map onto an orbifold curve whose orbifold fundamental group is nontrivial. We construct an example of a cyclic cover of the projective plane which is an abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating the extent to which these conditions are necessary.

The wall-crossing behavior for Bridgeland’s stability conditions on abelian and K3 surfaces

2018 ◽  
Vol 2018 (735) ◽  
pp. 1-107 ◽  
Author(s):  
Hiroki Minamide ◽  
Shintarou Yanagida ◽  
Kōta Yoshioka
Keyword(s):  
Stability Condition ◽  
Derived Category ◽  
The Other ◽  
Abelian Surface ◽  
Stability Conditions ◽  
Abelian Surfaces ◽  
Coherent Sheaves ◽  
Fundamental Properties ◽  
Wall Crossing ◽  
Wall Crossing Formula

AbstractThe wall-crossing behavior for Bridgeland’s stability conditions on the derived category of coherent sheaves on K3 or abelian surface is studied. We introduce two types of walls. One is called the wall for categories, where thet-structure encoded by stability condition is changed. The other is the wall for stabilities, where stable objects with prescribed Mukai vector may get destabilized. Some fundamental properties of walls and chambers are studied, including the behavior under Fourier–Mukai transforms. A wall-crossing formula of the counting of stable objects will also be derived. As an application, we will explain previous results on the birational maps induced by Fourier–Mukai transforms on abelian surfaces. These transformations turns out to coincide with crossing walls of certain property.

scholarly journals Kummer surfaces associated to (1, 2)-polarized abelian surfaces

2011 ◽  
Vol 202 ◽  
pp. 127-143
Author(s):  
Afsaneh Mehran
Keyword(s):  
Double Cover ◽  
Pezzo Surface ◽  
Abelian Surface ◽  
Kummer Surface ◽  
Abelian Surfaces ◽  
Del Pezzo Surface ◽  
Singular Fibers ◽  
Kummer Surfaces ◽  
Del Pezzo

AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of typeI2.

Against the Yuck Factor: On the Ideal Role of Disgust in Society

Utilitas ◽  
2014 ◽  
Vol 26 (2) ◽  
pp. 153-177 ◽  
Author(s):  
DANIEL KELLY ◽  
NICOLAE MORAR
Keyword(s):  
Social Work ◽  
Political Institutions ◽  
Empirical Theory ◽  
Normative Issues ◽  
In Virtue Of ◽  
The Ideal

The view we defend is that in virtue of its nature, disgust is not fit to do any moral or social work whatsoever, and that there are no defensible uses for disgust in legal or political institutions. We first describe our favoured empirical theory of the nature of disgust. Turning from descriptive to normative issues, we address the best arguments in favour of granting disgust the power to justify certain judgements, and to serve as a social tool, respectively. Daniel Kahan advances a pair of theses that suggest disgust is indispensable (Moral Indispensability Thesis), and so has an important part to play in the functioning of a just, well-ordered society (Conservation Thesis). We develop responses and show how they rebut the arguments given in support of each thesis. We conclude that any society free of social disgust would be more just, reasonable and compassionate.

scholarly journals On the structure of local cohomology modules for monomial curves in

1994 ◽  
Vol 136 ◽  
pp. 81-114 ◽  
Author(s):  
H. Bresinsky ◽  
F. Curtis ◽  
M. Fiorentini ◽  
L. T. Hoa
Keyword(s):  
Local Cohomology ◽  
Closed Field ◽  
Ideal Sheaf ◽  
Homogeneous Ideal ◽  
Local Cohomology Module ◽  
Algebraic Set ◽  
Monomial Curves ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
The Ideal

Our setting for this paper is projective 3-space over an algebraically closed field K. By a curve C ⊂ is meant a 1-dimensional, equidimensional projective algebraic set, which is locally Cohen-Macaulay. Let be the Hartshorne-Rao module of finite length (cf. [R]). Here Z is the set of integers and ℐc the ideal sheaf of C. In [GMV] it is shown that , where is the homogeneous ideal of C, is the first local cohomology module of the R-module M with respect to . Thus there exists a smallest nonnegative integer k ∊ N such that , (see also the discussion on the 1-st local cohomology module in [GW]). Also in [GMV] it is shown that k = 0 if and only if C is arithmetically Cohen-Macaulay and C is arithmetically Buchsbaum if and only if k ≤ 1. We therefore have the following natural definition.

scholarly journals Hyper-K\"ahler Fourfolds Fibered by Elliptic Products

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Ljudmila Kamenova
Keyword(s):  
Elliptic Curves ◽  
Abelian Surface ◽  
Abelian Surfaces ◽  
Genus Two

Every fibration of a projective hyper-K\"ahler fourfold has fibers which are Abelian surfaces. In case the Abelian surface is a Jacobian of a genus two curve, these have been classified by Markushevich. We study those cases where the Abelian surface is a product of two elliptic curves, under some mild genericity hypotheses. Comment: 8 pages, EPIGA published version

scholarly journals The Value of Information

2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Martin J Vilela
Keyword(s):  
Decision Tree ◽  
Value Of Information ◽  
Imperfect Information ◽  
Lack Of Information ◽  
New Information ◽  
Input Parameters ◽  
Additional Form ◽  
The Ideal

Value of information is a methodology that aims to determine whether it is worth acquiring new information. The acquisition of new data may reduce the uncertainties of the input parameters that define the value of a project. Such a reduction can increase our expectations and consequently the value of the project. The acquisition of data is justifiable only if their cost is less than the project value increases due to an increase in the certainty of the parameters. This article reviews the concepts and methodology of the value of information when the uncertainty is due to a lack of information and discusses an example of this methodology. A decision tree is built for the ideal perfect and imperfect information cases in the example shown and both results are contrasted. It is shown that, in the example discussed, it is worth acquiring the data if their cost is less than the calculated threshold. This article also introduces an additional form of uncertainty that occurs because of ambiguity and will be discussed in a future article.

scholarly journals American Dream Revisited: A Media Discourse Representation in Cognitive-linguistic Perspective

2021 ◽  
Vol 13 (4) ◽  
Author(s):  
Svitlana Lyubymova ◽  
Keyword(s):  
American Dream ◽  
Corpus Analysis ◽  
Media Discourse ◽  
Discourse Representation ◽  
Cultural Experience ◽  
Cognitive Linguistic ◽  
Complex Phenomena ◽  
Linguistic Approach ◽  
In Virtue Of ◽  
The Ideal

Considered in cognitive-linguistic perspective, “American Dream” is a represented in media discourse stereotype that embodies ideal of happiness in a prosperous democratic society. The research methodology rests on the premise of cognitive-linguistic approach to study of sociocultural stereotypes, which are seen as complex phenomena of social and cultural experience, manifested in behavioural, material, and verbal codes. Methodological tools of discursive and corpus analysis proved the variability of meaning of the stereotype. In the course of time, it shows semantic changes, conditioned by socio-economic and cultural factors. Empirical study eventuates in distinguishing three periods that correlate with transformation of the stereotype. The period of formation outlines the ideal of freedom and equality. The next period, which started in the 1950s, manifested changes toward obtaining happiness only in virtue of wealth. In recent years, “American Dream” is being associated more with freedom of choice than mere financial success.

scholarly journals Lexical Characteristics of the Translation of the Russian Newspapers: "Komsomolskaya Pravda" as Example Лексические особенности перевода газетных заголовков (На материале газеты «Комсомольская правда»)

2022 ◽  
Vol 0 (45) ◽  
pp. 210-232
Author(s):  
Fatima Ali Aglan ◽  
◽  
Ali Adnan Mashosh ◽  
Keyword(s):  
New Information ◽  
Lexical Items ◽  
The Ideal

The present study discusses the semantic characteristics of the Russian newspapers journalistic headlines (The Russian newspaper "Komsomolskaya Pravda" as Example"). The study traces the characteristics of the Russian newspaper headlines, its relevance to grammar, syntax, lexical items and style. These characteristics in Russian will be investigated and compared to their Arabic correspondents in the process of translation. The study also specifies the meanings and the functions of the newspaper headlines in the light of modern linguistics stressing the grammatical, lexical and stylistic aspects of headlines translation from Russian into Arabic. Journalistic headline reports a piece of information of a piece of news, presents, neutrally, new information related to the main story. The ideal headline is characterized by being composed of only few words carrying lots of significance. Its relevance to the news ought to be clear and answers several inquiries about the story, including: Who, What, When, Where, How and What for. Аннотация Статья посвящена вопросу особенности русского газетного заголовка, обусловлены нормами грамматики, лексики и стиля. Будут выявлены, какие соответствия этим особенностям существуют в русском языке. в статье будет определены значения и функций газетных заголовков в современной лингвистике. А также будет обсуждены Лексико-грамматические и стилистические аспекты при переводе заголовков с русского языка на арабский язык.. заголовок несет информацию по сопутствующей теме и предоставляет новую информацию, относящуюся к основным новостям, с полной беспристрастностью, а идеальный заголовок новости состоит из нескольких слов с множеством коннотаций, а заголовок новости отличается четкой новостной значимостью. поскольку он отвечает на ряд основных вопросов в новостях, в том числе: Кто? и что? И когда? Где? Как? Почему?

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