scholarly journals Dynamical invariants of monomial correspondences

2020 ◽  
pp. 1-16
Author(s):  
NGUYEN-BAC DANG ◽  
ROHINI RAMADAS
Keyword(s):  
Exponential Growth ◽  
Toric Varieties ◽  
Arithmetic Geometry ◽  
Degree Sequences ◽  
Asymptotic Rate ◽  
Dynamical Invariants ◽  
Dynamical Degrees

We focus on various dynamical invariants associated to monomial correspondences on toric varieties, using algebraic and arithmetic geometry. We find a formula for their dynamical degrees, relate the exponential growth of the degree sequences to a strict log-concavity condition on the dynamical degrees and compute the asymptotic rate of the growth of heights of points of such correspondences.

Design emergence in Morocco as an African country: a pending institutionalization

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Nabil EL HILALI
Keyword(s):  
Institutional Theory ◽  
Exponential Growth ◽  
African Country ◽  
Political Stability ◽  
The State ◽  
Design Management ◽  
Specific Context ◽  
Developed Economies ◽  
Design Value ◽  
Specific Country

If design management is worldwide institutionalized especially in developed economies, little is known about African design even though the continent is becoming an attractive economy thanks to his exponential growth and more political stability. Oriented toward one specific country: Morocco, this study through a questioning embedded in institutional theory brings an overview about design in a specific context. This research captures design management emergence in Morocco by spotting the light on the state of design institutionalization toward the creation of design value.

Won’t you self-confine for two weeks to save a town? Delaying exponential growth.

2020 ◽  
Author(s):  
Michal Levy ◽  
David Leiser ◽  
Avia Spivak
Keyword(s):  
Exponential Growth ◽  
Short Delay

Much of the communication around the current pandemic stresses the exponential growth in the number of infections. We observe that this approach may backfire: it becomes difficult to convince people to obey strict constraints when what will be achieved is merely a short delay in that growth. Based on a method we successfully used in a context of pension savings, we suggest how best to frame the gains of delaying tactics

scholarly journals Codimension bounds for the Noether–Lefschetz components for toric varieties

2021 ◽  
Author(s):  
Ugo Bruzzo ◽  
William D. Montoya
Keyword(s):  
Irreducible Component ◽  
Toric Variety ◽  
Toric Varieties ◽  
Ample Divisor ◽  
Smooth Hypersurface

AbstractFor a quasi-smooth hypersurface X in a projective simplicial toric variety $$\mathbb {P}_{\Sigma }$$ P Σ , the morphism $$i^*:H^p(\mathbb {P}_{\Sigma })\rightarrow H^p(X)$$ i ∗ : H p ( P Σ ) → H p ( X ) induced by the inclusion is injective for $$p=\dim X$$ p = dim X and an isomorphism for $$p<\dim X-1$$ p < dim X - 1 . This allows one to define the Noether–Lefschetz locus $$\mathrm{NL}_{\beta }$$ NL β as the locus of quasi-smooth hypersurfaces of degree $$\beta $$ β such that $$i^*$$ i ∗ acting on the middle algebraic cohomology is not an isomorphism. We prove that, under some assumptions, if $$\dim \mathbb {P}_{\Sigma }=2k+1$$ dim P Σ = 2 k + 1 and $$k\beta -\beta _0=n\eta $$ k β - β 0 = n η , $$n\in \mathbb {N}$$ n ∈ N , where $$\eta $$ η is the class of a 0-regular ample divisor, and $$\beta _0$$ β 0 is the anticanonical class, every irreducible component V of the Noether–Lefschetz locus quasi-smooth hypersurfaces of degree $$\beta $$ β satisfies the bounds $$n+1\leqslant \mathrm{codim}\,Z \leqslant h^{k-1,\,k+1}(X)$$ n + 1 ⩽ codim Z ⩽ h k - 1 , k + 1 ( X ) .

scholarly journals 2nd Edition of Instrumenting Smart City Applications with Big Sensing and Earth Observatory Data: Tools, Methods and Techniques

2021 ◽  
Vol 13 (7) ◽  
pp. 1310
Author(s):  
Gabriele Bitelli ◽  
Emanuele Mandanici
Keyword(s):  
High Resolution ◽  
Exponential Growth ◽  
Smart City ◽  
Earth Observation ◽  
Urban Environments ◽  
Observation Data ◽  
High Resolution Imagery ◽  
Observatory Data ◽  
Methods And Techniques ◽  
Earth Observation Data

The exponential growth in the volume of Earth observation data and the increasing quality and availability of high-resolution imagery are increasingly making more applications possible in urban environments [...]

scholarly journals On the Hodge conjecture for quasi-smooth intersections in toric varieties

2021 ◽  
Author(s):  
Ugo Bruzzo ◽  
William Montoya
Keyword(s):  
Complete Intersection ◽  
Toric Variety ◽  
Toric Varieties ◽  
Picard Group ◽  
Hodge Conjecture ◽  
Smooth Hypersurface ◽  
Suitable Notion

AbstractWe establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection subvarieties in the toric environment, and in particular quasi-smooth hypersurfaces. We show that under appropriate conditions, the Hodge conjecture holds for a very general quasi-smooth intersection subvariety, generalizing the work on quasi-smooth hypersurfaces of the first author and Grassi in Bruzzo and Grassi (Commun Anal Geom 28: 1773–1786, 2020). We also show that the Hodge Conjecture holds asymptotically for suitable quasi-smooth hypersurface in the Noether–Lefschetz locus, where “asymptotically” means that the degree of the hypersurface is big enough, under the assumption that the ambient variety $${{\mathbb {P}}}_\Sigma ^{2k+1}$$ P Σ 2 k + 1 has Picard group $${\mathbb {Z}}$$ Z . This extends to a class of toric varieties Otwinowska’s result in Otwinowska (J Alg Geom 12: 307–320, 2003).

scholarly journals Embedding the Picard group inside the class group: the case of $$\mathbb {Q}$$-factorial complete toric varieties

2021 ◽  
Author(s):  
Michele Rossi ◽  
Lea Terracini
Keyword(s):  
Free Group ◽  
Toric Variety ◽  
Class Group ◽  
Abelian Groups ◽  
Toric Varieties ◽  
Picard Group ◽  
Closed Field ◽  
Finitely Generated ◽  
Free Part ◽  
Canonical Injection

AbstractLet X be a $$\mathbb {Q}$$ Q -factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group $$\mathrm{Pic}(X)$$ Pic ( X ) in the group $$\mathrm{Cl}(X)$$ Cl ( X ) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $$\mathrm{Pic}(X)$$ Pic ( X ) in $$\mathrm{Cl}(X)$$ Cl ( X ) is contained in a free part of the latter group.

Sign in / Sign up

Export Citation Format

Share Document