Cremona Transformations with Smooth Irreducible Fundamental Locus

1989 ◽  
Vol 111 (2) ◽  
pp. 289 ◽  
Author(s):  
Bruce Crauder ◽  
Sheldon Katz
Keyword(s):  
Cremona Transformations

scholarly journals On the monomial birational maps of the projective space

2003 ◽  
Vol 75 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Gérard Gonzalez-Sprinberg ◽  
Ivan Pan
Keyword(s):  
Projective Space ◽  
Group Structure ◽  
Cremona Transformations ◽  
Birational Maps

We describe the group structure of monomial Cremona transformations. It follows that every element of this group is a product of quadratic monomial transformations, and geometric descriptions in terms of fans.

On certain Cremona transformations in circle-space connected with the Miquel-Clifford configuration

1937 ◽  
Vol 33 (1) ◽  
pp. 21-25 ◽  
Author(s):  
A. Narasinga Rao
Keyword(s):  
Common Point ◽  
Cremona Transformations ◽  
Straight Lines

The classical configuration connected with the names of Miquel and Clifford associates with a set of n straight lines in a plane a point called their Miquel point when n is even, and a circle, their Clifford circle, when n is odd. When the number of lines n in a set is even, the omission of these, one at a time, gives n subsets whose associated Clifford circles are concurrent at the Miquel point of the original set; when n is odd, the omission of the lines one at a time gives n subsets whose associated Miquel points are concyclic on the Clifford circle of the original set. To start the chain, it is only necessary to define the Miquel point of two lines as their common point.

scholarly journals Special cubic Cremona transformations of ℙ6 and ℙ7

2019 ◽  
Vol 19 (2) ◽  
pp. 191-204 ◽  
Author(s):  
Giovanni Staglianò
Keyword(s):  
Cremona Transformation ◽  
Cremona Transformations ◽  
Base Locus ◽  
Famous Result

Abstract A famous result of Crauder and Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. They also proved that a special Cremona transformation with base locus of dimension three has to be one of the following: 1) a quinto-quintic transformation of ℙ5; 2) a cubo-quintic transformation of ℙ6; or 3) a quadro-quintic transformation of ℙ8. Special Cremona transformations as in Case 1) have been classified by Ein and Shepherd-Barron (1989), while in our previous work (2013), we classified special quadro-quintic Cremona transformations of ℙ8. Here we consider the problem of classifying special cubo-quintic Cremona transformations of ℙ6, concluding the classification of special Cremona transformations whose base locus has dimension three.

Specialization of Cremona transformations

Mathematika ◽  
1968 ◽  
Vol 15 (2) ◽  
pp. 171-177 ◽  
Author(s):  
J. G. Semple ◽  
J. A. Tyrrell
Keyword(s):  
Cremona Transformations

On singular quadratic complexes, quintic curves and Cremona transformations

2012 ◽  
Vol 61 (2) ◽  
pp. 201-240
Author(s):  
Dan Avritzer ◽  
Gerard Gonzalez-Sprinberg ◽  
Ivan Pan
Keyword(s):  
Cremona Transformations ◽  
Quintic Curves

scholarly journals Identifiability of homogeneous polynomials and Cremona transformations

2019 ◽  
Vol 2019 (757) ◽  
pp. 279-308 ◽  
Author(s):  
Francesco Galuppi ◽  
Massimiliano Mella
Keyword(s):  
Special Class ◽  
Homogeneous Polynomial ◽  
Projective Spaces ◽  
Homogeneous Polynomials ◽  
Additive Decomposition ◽  
Linear Forms ◽  
Cremona Transformations ◽  
General Polynomial ◽  
Powers Of Linear Forms

AbstractA homogeneous polynomial of degree d in {n+1} variables is identifiable if it admits a unique additive decomposition in powers of linear forms. Identifiability is expected to be very rare. In this paper we conclude a work started more than a century ago and we describe all values of d and n for which a general polynomial of degree d in {n+1} variables is identifiable. This is done by classifying a special class of Cremona transformations of projective spaces.

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