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1
Geometry of the Plane Cremona Maps
Hence the homaloidal curve C must be a component of D. But since there are
infinite irreducible homaloidal curves in C (2.1.3), we reach a contradiction. D As
it was announced in advance in the previous section, 5.3.1 and 5.2.20 together ...
Maria Alberich-Carraminana, 2002
2
Geometry of Four Dimensions
CHAPTER XI. Curves in jv-Fold Homaloidal Space. In this chapter, the results
relating to the principal homaloidal amplitudes connected with a skew curve in ?t-
fold homaloidal space are merely stated, usually without the contributory analysis
.
3
Lectures on Curves, Surfaces and Projective Varieties: A ...
We now give a brief discussion of a method, first suggested by L. Cremona [29], [
30], for determining (if they exist) all the homaloidal systems of surfaces in P3 that
contain a given (rational) surface Fo having a known representation over a ...
4
Bulletin of the National Research Council
A surface <f> of a homaloidal web is cut by the other surfaces of the web in a
homaloidal net of curves on <j>. Since <f> is rational it can be mapped on a
plane ir by a net 2 of curves of order r on a certain base B. All surfaces of order n
cut <£ in ...
5
Selected Topics in Algebraic Geometry
The first general method for obtaining a wide variety of transformations in space
is due to Cre- mona(2s). A surface ,f, of a homaloidal web is cut by the other
surfaces of the web in a homaloidal net of curves on ,£. Since n£ is rational it can
be ...
6
Geometry of Four Dimenions
The purpose of this chapter* is to sketch, though only in brief outline, the different
kinds of measures of the curvature of an amplitude of n dimensions, existing in a
homaloidal space of n + 1 dimensions which will be called the plenary space.
7
Classical Algebraic Geometry: A Modern View
Lemma 7.5.14 Let v be a proper homaloidal type. Then it belongs to the W(N)-
orbit of the vector e0. Proof Let be a proper homaloidal type and be the
corresponding homaloidal bubble cycle. Let w 6 W(N) and v' I w(v) I . We have m,
- I ei ~ v'I ...
8
Understanding Space-Time: The Philosophical Development of ...
Space-time in which there is no gravitational field which cannot be transformed
away is called homaloidal . . . Our space is not like that, though we believe that at
great distances from all gravitating matter it tends toward this condition as a limit.
9
Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. ...
2.1 Homaloidal linear systems We will be working over the field of complex
numbers. Recall that a dominant rational map χ : P2− → P2 is given by a 2-
dimensional linear system H equal to the proper transform of the linear system of
lines H ...
Yuri Tschinkel, Yuri Zarhin, 2010
10
Algebraic Curves over a Finite Field
In this case, the transformation to is birational; it is also called a Cremona
transformation. Then through the points P0, P1, . . . , Pnzzl pass all curves of the
net Q This is therefore a homaloidal net', that is, every two of its curves have a
single ...
J. W.P. Hirschfeld, G. Korchmáros, F. Torres, 2013
