# Notes on the Evolution of Complete Correlations

• Dan Laksov
Chapter
Part of the Progress in Mathematics book series (PM, volume 24)

## Abstract

1. The problem of correlations between two d-dimensional spaces in an n-dimensional space can be stated in the following way: “In a projective space [n] of dimension n, determine all the pairs of linear subspaces Sd and S’d of dimension d together with a correlation between them, such that Sd and S’d satisfy given Schubert conditions a0,a1,…,ad and a’0,a’1,…,a’d respectively, and the correlation satisfies a composite condition $$\mu _{0}^{{{n_{0}}}},\mu _{1}^{{{n_{2}}}}, \ldots ,\mu _{{d - 1}}^{{{n_{{d - 1}}}}}$$ where
$$\Sigma _{{i = 0}}^{d}({a_{i}} + a_{i}^{!}) + d = \Sigma _{{i = 0}}^{d}{\text{ }}{n_{i}}$$
and where μi is the condition that the two i-dimensional spaces in which Sd and S’d in general meet two fixed linear spaces Rn-d+i and R’n-d+i respectively, are conjugate under the correlation.”

## Keywords

Singular Point Singular Line Complete Correlation Exceptional Locus Monoidal Transformation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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