scholarly journals Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yang Gao ◽  
Heping Zhang
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Clar Number ◽  
Clar Structure ◽  
Fries Number

Fowler and Pisanski showed that the Fries number for a fullerene on surface Σ is bounded above by|V|/3, and fullerenes which attain this bound are exactly the class of leapfrog fullerenes on surface Σ. We showed that the Clar number of a fullerene on surface Σ is bounded above by(|V|/6)-χ(Σ), whereχ(Σ)stands for the Euler characteristic of Σ. By establishing a relation between the extremal fullerenes and the extremal (4,6)-fullerenes on the sphere, Hartung characterized the fullerenes on the sphereS0for which Clar numbers attain(|V|/6)-χ(S0). We prove that, for a (4,6)-fullerene on surface Σ, its Clar number is bounded above by(|V|/6)+χ(Σ)and its Fries number is bounded above by(|V|/3)+χ(Σ), and we characterize the (4,6)-fullerenes on surface Σ attaining these two bounds in terms of perfect Clar structure. Moreover, we characterize the fullerenes on the projective planeN1for which Clar numbers attain(|V|/6)-χ(N1)in Hartung’s method.

scholarly journals Indecomposable branched coverings over the projective plane by surfaces M with χ(M) ≤ 0

2018 ◽  
Vol 27 (05) ◽  
pp. 1850030
Author(s):  
Natalia A. Viana Bedoya ◽  
Daciberg Lima Gonçalves ◽  
Elena A. Kudryavtseva
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Covering Surface ◽  
Branched Coverings ◽  
Branched Covering

In this work, we study the decomposability property of branched coverings of degree [Formula: see text] odd, over the projective plane, where the covering surface has Euler characteristic [Formula: see text]. The latter condition is equivalent to say that the defect of the covering is greater than [Formula: see text]. We show that, given a datum [Formula: see text] with an even defect greater than [Formula: see text], it is realizable by an indecomposable branched covering over the projective plane. The case when [Formula: see text] is even is known.

scholarly journals Counting the number of trigonal curves of genus 5 over finite fields

2020 ◽  
Vol 208 (1) ◽  
pp. 31-48
Author(s):  
Thomas Wennink
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Euler Characteristic ◽  
Finite Fields ◽  
Moduli Space ◽  
Plane Curves ◽  
Sieve Method ◽  
Main Application ◽  
Trigonal Curves

AbstractThe trigonal curves of genus 5 can be represented by projective plane quintics that have one singularity of delta invariant one. Combining this with a partial sieve method for plane curves we count the number of such curves over any finite field. The main application is that this gives the motivic Euler characteristic of the moduli space of trigonal curves of genus 5.

scholarly journals BRILL–NOETHER THEOREMS AND GLOBALLY GENERATED VECTOR BUNDLES ON HIRZEBRUCH SURFACES

2018 ◽  
Vol 238 ◽  
pp. 1-36 ◽  
Author(s):  
IZZET COSKUN ◽  
JACK HUIZENGA
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Chern Class ◽  
Vector Bundles ◽  
Betti Numbers ◽  
Stable Bundle ◽  
Hirzebruch Surface ◽  
Hirzebruch Surfaces ◽  
Chern Characters ◽  
First Chern Class

In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we compute the Betti numbers of a general stable bundle. We also show that a general stable bundle on a Hirzebruch surface has a special resolution generalizing the Gaeta resolution on the projective plane. As a consequence of these results, we classify Chern characters such that the general stable bundle is globally generated.

scholarly journals Matroid Duality from Topological Duality in Surfaces of Nonnegative Euler Characteristic

2002 ◽  
Vol 11 (5) ◽  
pp. 515-528 ◽  
Author(s):  
DANIEL C. SLILATY
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Connected Graph ◽  
Dual Graph ◽  
Topological Duality ◽  
Element Set

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

scholarly journals Group-labeled light dual multinets in the projective plane

2018 ◽  
Vol 341 (8) ◽  
pp. 2121-2130 ◽  
Author(s):  
Gábor Korchmáros ◽  
Gábor P. Nagy
Keyword(s):  
Projective Plane
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