scholarly journals Classification of optimal quaternary Hermitian LCD codes of dimension $2$

2020 ◽  
pp. 229-236
Author(s):  
Keita ISHIZUKA
Keyword(s):  
Lcd Codes ◽  
Dimension 2

Classification of Estimation Algebras with State Dimension 2

2006 ◽  
Vol 45 (3) ◽  
pp. 1039-1073 ◽  
Author(s):  
Xi Wu ◽  
Stephen S.‐T. Yau
Keyword(s):  
Dimension 2

Algebraic Surfaces and the Miyaoka-Yau Inequality

2017 ◽  
Author(s):  
Paula Tretkoff
Keyword(s):  
Differential Geometry ◽  
Algebraic Surface ◽  
Smooth Surface ◽  
General Type ◽  
Kodaira Dimension ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Smooth Complex ◽  
Dimension 2

This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.

scholarly journals Characterization and classification of optimal LCD codes

2021 ◽  
Author(s):  
Makoto Araya ◽  
Masaaki Harada ◽  
Ken Saito
Keyword(s):  
Lcd Codes

scholarly journals About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane

2021 ◽  
Vol 38 ◽  
pp. 54-64
Author(s):  
P. A. Shaikhullina ◽  
Keyword(s):  
Vector Field ◽  
Normal Form ◽  
Vector Fields ◽  
The Other ◽  
Time Shift ◽  
Saddle Node ◽  
Dimension 2 ◽  
The One

There are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or one). In this paper, the first stage of constructing an analytical classification by the method of functional invariants is carried out: a theorem on the reducibility of a germ to its formal normal form by "semiformal" changes of coordinates is proved. The one-time shift along the saddle node vector field (the formal normal form in the problem of the analytical classification of saddle-node vector fields on a plane) is chosen as the formal normal form.

Topological classification of simplest Gorenstein non-complete intersection singularities of dimension 2

2015 ◽  
Vol 19 (4) ◽  
pp. 651-792
Author(s):  
Stephen S.-T. Yau ◽  
Mingyi Zhang ◽  
Huaiqing Zuo
Keyword(s):  
Complete Intersection ◽  
Topological Classification ◽  
Dimension 2

Classification of Balinsky–Novikov superalgebras with dimension 2|2

2012 ◽  
Vol 45 (22) ◽  
pp. 225201 ◽  
Author(s):  
Yan Wang ◽  
Zhiqi Chen ◽  
Chengming Bai
Keyword(s):  
Dimension 2

Principal bundles on two-dimensional CW-complexes with disconnected structure group

2022 ◽  
pp. 1-16
Author(s):  
André G. Oliveira
Keyword(s):  
Lie Group ◽  
Classical Result ◽  
Topological Classification ◽  
Characteristic Classes ◽  
Classifying Space ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Dimension 2 ◽  
Disconnected Structure

Abstract Given any topological group G, the topological classification of principal G-bundles over a finite CW-complex X is long known to be given by the set of free homotopy classes of maps from X to the corresponding classifying space BG. This classical result has been long-used to provide such classification in terms of explicit characteristic classes. However, even when X has dimension 2, there is a case in which such explicit classification has not been explicitly considered. This is the case where G is a Lie group, whose group of components acts nontrivially on its fundamental group $\pi_1G$ . Here, we deal with this case and obtain the classification, in terms of characteristic classes, of principal G-bundles over a finite CW-complex of dimension 2, with G is a Lie group such that $\pi_0G$ is abelian.

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