scholarly journals A comparison of positivity in complex and tropical toric geometry

2021 ◽  
Author(s):  
José Ignacio Burgos Gil ◽  
Walter Gubler ◽  
Philipp Jell ◽  
Klaus Künnemann
Keyword(s):  
Toric Variety ◽  
Subsequent Paper ◽  
Toric Geometry ◽  
Plurisubharmonic Functions ◽  
Smooth Complex ◽  
Positive Currents ◽  
Complex Forms ◽  
Correspondence Theorem

AbstractGiven a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford–Taylor theory of plurisubharmonic functions on the tropicalization.

scholarly journals LOCAL VANISHING AND HODGE FILTRATION FOR RATIONAL SINGULARITIES

2018 ◽  
Vol 19 (3) ◽  
pp. 801-819
Author(s):  
Mircea Mustaţă ◽  
Sebastián Olano ◽  
Mihnea Popa
Keyword(s):  
Toric Variety ◽  
Exceptional Divisor ◽  
Resolution Of Singularities ◽  
Isolated Singularities ◽  
Rational Singularities ◽  
Smooth Complex ◽  
Hodge Filtration ◽  
Generation Level ◽  
Image Position

Given an $n$-dimensional variety $Z$ with rational singularities, we conjecture that if $f:Y\rightarrow Z$ is a resolution of singularities whose reduced exceptional divisor $E$ has simple normal crossings, then $$\begin{eqnarray}\displaystyle R^{n-1}f_{\ast }\unicode[STIX]{x1D6FA}_{Y}(\log E)=0. & & \displaystyle \nonumber\end{eqnarray}$$ We prove this when $Z$ has isolated singularities and when it is a toric variety. We deduce that for a divisor $D$ with isolated rational singularities on a smooth complex $n$-dimensional variety $X$, the generation level of Saito’s Hodge filtration on the localization $\mathscr{O}_{X}(\ast D)$ is at most $n-3$.

scholarly journals Correspondence theorems via tropicalizations of moduli spaces

2016 ◽  
Vol 18 (03) ◽  
pp. 1550043 ◽  
Author(s):  
Andreas Gross
Keyword(s):  
Moduli Spaces ◽  
Toric Variety ◽  
Algebraic Curves ◽  
Rational Curves ◽  
Tropical Curves ◽  
Algebraic Tori ◽  
Pass Through ◽  
General Correspondence ◽  
Correspondence Theorem ◽  
Generic Points

We show that the moduli spaces of irreducible labeled parametrized marked rational curves in toric varieties can be embedded into algebraic tori such that their tropicalizations are the analogous tropical moduli spaces. These embeddings are shown to respect the evaluation morphisms in the sense that evaluation commutes with tropicalization. With this particular setting in mind, we prove a general correspondence theorem for enumerative problems which are defined via “evaluation maps” in both the algebraic and tropical world. Applying this to our motivational example, we show that the tropicalizations of the curves in a given toric variety which intersect the boundary divisors in their interior and with prescribed multiplicities, and pass through an appropriate number of generic points are precisely the tropical curves in the corresponding tropical toric variety satisfying the analogous condition. Moreover, the intersection-theoretically defined multiplicities of the tropical curves are equal to the numbers of algebraic curves tropicalizing to them.

scholarly journals Duality of positive currents and plurisubharmonic functions in calibrated geometry

2009 ◽  
Vol 131 (5) ◽  
pp. 1211-1239 ◽  
Author(s):  
F. Reese Harvey ◽  
H. Blaine Lawson Jr.
Keyword(s):  
Plurisubharmonic Functions ◽  
Positive Currents ◽  
Calibrated Geometry

Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations

2019 ◽  
Vol 31 (6) ◽  
pp. 1457-1466
Author(s):  
Takayuki Koike
Keyword(s):  
Line Bundle ◽  
Elliptic Curve ◽  
Positive Curvature ◽  
Complex Surface ◽  
Holomorphic Foliation ◽  
Hermitian Metric ◽  
Plurisubharmonic Functions ◽  
Smooth Complex ◽  
Normal Bundles ◽  
Dynamical Properties

AbstractLet C be a smooth elliptic curve embedded in a smooth complex surface X such that C is a leaf of a suitable holomorphic foliation of X. We investigate the complex analytic properties of a neighborhood of C under some assumptions on the complex dynamical properties of the holonomy function. As an application, we give an example of {(C,X)} in which the line bundle {[C]} is formally flat along C, however it does not admit a {C^{\infty}} Hermitian metric with semi-positive curvature. We also exhibit a family of embeddings of a fixed elliptic curve for which the positivity of normal bundles does not behave in a simple way.

Organization of the Pellicle and the Muciferous Glands in Euglena Gracilis

1970 ◽  
Vol 28 ◽  
pp. 104-105
Author(s):  
Hilton H. Mollenhauer ◽  
W. Evans
Keyword(s):  
Plasma Membrane ◽  
Euglena Gracilis ◽  
Complex Forms ◽  
Secondary Periodicity

The pellicular structure of Euglena gracilis consists of a series of relatively rigid strips (Fig. 1) composed of ridges and grooves which are helically oriented along the cell and which fuse together into a common junction at either end of the cell. The strips are predominantly protein and consist in part of a series of fibers about 50 Å in diameter spaced about 85 Å apart and with a secondary periodicity of about 450 Å. Microtubules are also present below each strip (Fig. 1) and are often considered as part of the pellicular complex. In addition, there may be another fibrous component near the base of the pellicle which has not yet been very well defined.The pellicular complex lies underneath the plasma membrane and entirely within the cell (Fig. 1). Each strip of the complex forms an overlapping junction with the adjacent strip along one side of each groove (Fig. 1), in such a way that a certain amount of sideways movement is possible between one strip and the next.

Making gender visible in family business: past and present

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Paloma Fernández Pérez ◽  
Eleanor Hamilton
Keyword(s):  
Family Business ◽  
Family Firms ◽  
Business Leadership ◽  
Legal Rules ◽  
Developed Economies ◽  
The Family ◽  
Interdisciplinary Synthesis ◽  
Complex Forms ◽  
Rules Of The Game

This  study  contributes  to  developing  our understanding of gender and family business. It draws on studies from the business history and management literatures and provides an interdisciplinary synthesis. It illuminates the role of women and their participation in the entrepreneurial practices of the family and the business. Leadership is introduced as a concept to examine the roles of women and men in family firms, arguing that concepts used  by  historians or economists like ownership and management have served to make women ‘invisible’, at least in western developed economies in which owners and managers have been historically due to legal rules  of  the  game  men,  and  minoritarily women. Finally, it explores gender relations and  the  notion  that  leadership  in  family business  may  take  complex  forms  crafte within constantly changing relationships.

How to grow a self: development of the self in a Bayesian brain

2019 ◽  
Author(s):  
Mateusz Wozniak
Keyword(s):  
Conceptual Development ◽  
Human Life ◽  
Predictive Coding ◽  
Body Representation ◽  
Developmental Trajectory ◽  
The Self ◽  
Learning Mechanisms ◽  
Bayesian Brain ◽  
Third Person ◽  
Complex Forms

The last two decades have brought several attempts to explain the self as a part of the Bayesian brain, typically within the framework of predictive coding. However, none of these attempts have looked comprehensively at the developmental aspect of self-representation. The goal of this paper is to argue that looking at the developmental trajectory is crucial for understanding the structure of an adult self-representation. The paper argues that the emergence of the self should be understood as an instance of conceptual development, which in the context of a Bayesian brain can be understood as a process of acquisition of new internal models of hidden causes of sensory input. The paper proposes how such models might emerge and develop over the course of human life by looking at different stages of development of bodily and extra-bodily self-representations. It argues that the self arises gradually in a series of discrete steps: from first-person multisensory representations of one’s body to third-person multisensory body representation, and from basic forms of the extended and social selves to progressively more complex forms of abstract self-representation. It discusses how each of them might emerge based on domain-general learning mechanisms, while also taking into account the potential role of innate representations. Finally it suggests how the conceptual structure of self-representation might inform the debate about the structure of self-consciousness.

Complex forms of the ethnic identity

2020 ◽  
Vol 4 (2) ◽  
pp. 75-89
Author(s):  
J.S. Zamaraeva ◽  
Keyword(s):  
Ethnic Identity ◽  
Complex Forms

Das Werk als Entgrenzung. : Werkkomplex und Dynamik des Gesamtwerks

2021 ◽  
Vol 31 (1) ◽  
pp. 139-154
Author(s):  
Svetlana Efimova
Keyword(s):  
Dynamic Structure ◽  
Intermediate Stage ◽  
Literary Work ◽  
Theoretical Research ◽  
Semantic Composition ◽  
Complex Forms ◽  
Special Relevance ◽  
Reception Side

Abstract Im Kontext des neu aufgekommenen theoretischen Interesses für die Werkkategorie wird überwiegend das ,Einzelwerk‘ fokussiert. Im vorliegenden Aufsatz wird das heuristische Potenzial des Konzepts ,Gesamtwerk‘ als ein anderer Teil der Werkkategorie herausgearbeitet. Neben dem üblichen Aspekt eines ,Lebenswerks‘ schließt das Gesamtwerk vielfältige Werkkomplexe und Werkgruppierungen ein, die auf Produktions- oder Rezeptionsseite entstehen. Analysiert werden feste und variable Anordnungen, Ab- und Entgrenzungen zwischen Einzelwerken eines Autors, die das Gesamtwerk zu einem dynamischen Gefüge machen. Ein Werkkomplex bildet eine Zwischenstufe und ein Bindeglied zwischen ,Einzelwerk‘ und ,Gesamtwerk‘. Daher besitzt er eine besondere Relevanz für die semantische Zusammensetzung der Werkkategorie als Trias, deren Teile sich aufeinander beziehen: Opus – Werkkomplex – Œuvre.The newly arisen theoretical research on the literary work category focuses mainly on the ,single work‘. This paper argues for the heuristic potential of the ,oeuvre‘ as another part of the work category. In addition to the usual aspect of a ,life’s work‘, the oeuvre includes diverse work complexes and work groupings that emerge on the production or reception side. The paper analyzes a dynamic structure of the oeuvre: fixed and variable arrangements, boundaries and dissolution of borders between single works by the same author. A work complex forms an intermediate stage and a link between ,single work‘ and ,oeuvre‘. It therefore has a special relevance for the semantic composition of the work category as a triad, the parts of which refer to each other: single work – work complex – oeuvre.

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