The Projective Line

2004 ◽  
pp. 13-43
Author(s):  
Jean Fresnel ◽  
Marius van der Put
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

Bilinear three-cycles on the projective line

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

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
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