Bilinear three-cycles on the projective line

1987 ◽  
Vol 33 (1) ◽  
pp. 72-80
Author(s):  
T M. K Davison
Keyword(s):  
Projective Line

scholarly journals Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

2017 ◽  
Vol 4 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Martin de Borbon
Keyword(s):  
Vector Field ◽  
Einstein Metrics ◽  
Projective Line ◽  
Tangent Cones ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Complex Curves ◽  
Complex Dimensions ◽  
Irregular Case ◽  
Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

scholarly journals Monodromy of cyclic coverings of the projective line

2013 ◽  
Vol 197 (1) ◽  
pp. 1-45 ◽  
Author(s):  
T. N. Venkataramana
Keyword(s):  
Projective Line ◽  
Cyclic Coverings

Which Functor Is the Projective Line?

2003 ◽  
Vol 110 (7) ◽  
pp. 574-592
Author(s):  
Daniel K. Biss
Keyword(s):  
Projective Line

scholarly journals Lubin-Tate extensions and Carlitz module over a projective line: an explicit connection

2021 ◽  
Vol 22 (2) ◽  
pp. 90-103
Author(s):  
Nikita Vyacheslavovich Elizarov ◽  
Sergei Vladimirovich Vostokov
Keyword(s):  
Projective Line ◽  
Carlitz Module

Distributions of projective invariants and model-based machine vision

1996 ◽  
Vol 28 (03) ◽  
pp. 641-661 ◽  
Author(s):  
K. V. Mardia ◽  
Colin Goodall ◽  
Alistair Walder
Keyword(s):  
Machine Vision ◽  
Projective Transformation ◽  
Likelihood Estimation ◽  
Cauchy Distribution ◽  
Projective Line ◽  
Cross Ratio ◽  
Projective Invariants ◽  
Inference Problems ◽  
The Cross ◽  
Insight Into

In machine vision, objects are observed subject to an unknown projective transformation, and it is usual to use projective invariants for either testing for a false alarm or for classifying an object. For four collinear points, the cross-ratio is the simplest statistic which is invariant under projective transformations. We obtain the distribution of the cross-ratio under the Gaussian error model with different means. The case of identical means, which has appeared previously in the literature, is derived as a particular case. Various alternative forms of the cross-ratio density are obtained, e.g. under the Casey arccos transformation, and under an arctan transformation from the real projective line of cross-ratios to the unit circle. The cross-ratio distributions are novel to the probability literature; surprisingly various types of Cauchy distribution appear. To gain some analytical insight into the distribution, a simple linear-ratio is also introduced. We also give some results for the projective invariants of five coplanar points. We discuss the general moment properties of the cross-ratio, and consider some inference problems, including maximum likelihood estimation of the parameters.

ALGEBRAIC POINTS ON THE PROJECTIVE LINE

2008 ◽  
Vol 45 (6) ◽  
pp. 1635-1646 ◽  
Author(s):  
Su-Ion Ih
Keyword(s):  
Projective Line

scholarly journals Construction of New S-Box Using Action of Quotient of the Modular Group for Multimedia Security

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Imran Shahzad ◽  
Qaiser Mushtaq ◽  
Abdul Razaq
Keyword(s):  
Finite Field ◽  
Modular Group ◽  
Fibonacci Sequence ◽  
Projective Line ◽  
Multimedia Security ◽  
New Technique ◽  
Substitution Box ◽  
Nonlinear Component ◽  
Coset Diagrams ◽  
A New Technique

Substitution box (S-box) is a vital nonlinear component for the security of cryptographic schemes. In this paper, a new technique which involves coset diagrams for the action of a quotient of the modular group on the projective line over the finite field is proposed for construction of an S-box. It is constructed by selecting vertices of the coset diagram in a special manner. A useful transformation involving Fibonacci sequence is also used in selecting the vertices of the coset diagram. Finally, all the analyses to examine the security strength are performed. The outcomes of the analyses are encouraging and show that the generated S-box is highly secure.

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