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Compositio mathematica, ISSN 0010-437X, 07/2018, Volume 154, Issue 7, pp. 1508 - 1533
We exhibit a Cremona transformation of $\mathbb{P}^{4}$ such that the base loci of the map and its inverse are birational to K3 surfaces... 
K3 surfaces | Cremona transformations | derived equivalences | MATHEMATICS | Mathematics - Algebraic Geometry
Journal Article
International Journal of Solids and Structures, ISSN 0020-7683, 11/2018, Volume 152-153, pp. 272 - 293
.... Specifically, we describe a series of polar transformations and discuss them from a geometric and an algebraic standpoint... 
Structural design | Graphic statics | Reciprocal diagrams | Rankine | Cremona | Maxwell | Projective geometry | Airy stress function | Static equilibrium | Poncelet duality | MECHANICS | Usage | Visualization (Computers) | Analysis
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2016, Volume 282, Issue 1, pp. 223 - 245
Journal Article
Advances in Geometry, ISSN 1615-715X, 04/2019, Volume 19, Issue 2, pp. 191 - 204
A famous result of Crauder and Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two... 
14E07 | threefold | 14E05 | Cremona transformation | base locus | 14J30 | Loci | Transformations | Classification
Journal Article
Annals of Mathematics, ISSN 0003-486X, 07/2011, Volume 174, Issue 1, pp. 299 - 340
Journal Article
Journal of Noncommutative Geometry, ISSN 1661-6952, 2016, Volume 10, Issue 1, pp. 221 - 244
In this paper we generalize some classical birational transformations to the non-commutative case... 
Non-commutative surfaces | Sklyanin algebras | Cremona transform | Birational transformation | MATHEMATICS | MATHEMATICS, APPLIED | non-commutative surfaces | REGULAR ALGEBRAS | DIMENSION-3 | PHYSICS, MATHEMATICAL
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 1, pp. 55 - 77
Special birational transformations Phi : P-r -> Z defined by quadric hypersurfaces are studied by means of the variety of lines L-z subset of Pr-1 passing through a general point z is an element of Z... 
MATHEMATICS | VARIETIES | MANIFOLDS | CREMONA TRANSFORMATIONS | Mathematics - Algebraic Geometry
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 4/2018, Volume 193, Issue 1, pp. 73 - 88
We consider Cremona transformations $$\phi {:}\,{\mathbb P}^4\dashrightarrow {\mathbb P}^4$$ ϕ:P4⤏P4 which factorize through projections of a smooth complete intersection of quadrics... 
Geometry | 14E07 | 14M10 | Mathematics | Cremona transformations | Quadrics | Complete intersections
Journal Article
1932, Private edition., University of Chicago, 31
Book
Duke Mathematical Journal, ISSN 0012-7094, 2015, Volume 164, Issue 13, pp. 2539 - 2575
For an arbitrary associative unital ring R, let J(1) and J(2) be the following noncommutative, birational, partly defined involutions on the set M-3 (R) of 3 x... 
MATHEMATICS | free field | Hadamard matrix product | 16S50 | Cremona transformation | noncommutative identities | birational dynamics | 16S85 | matrices over noncommutative rings | noncommutative birational involutions | 16S38
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2015, Volume 65, Issue 6, pp. 2641 - 2680
.... Geometric properties of the elements of the group are given, as well as a description of its intersection with monomial transformations. 
Monomial transformations | Standard involution | Cremona transformation | Rational hypersurfaces | MATHEMATICS | monomial transformations | rational hypersurfaces | standard involution | SETS | Mathematics - Algebraic Geometry
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2014, Volume 64, Issue 1, pp. 71 - 111
It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra... 
Jordan algebra | Cremona transformation | MATHEMATICS | VARIETIES | ALGEBRAS | CURVES
Journal Article
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, ISSN 1120-6330, 2013, Volume 24, Issue 3, pp. 409 - 436
We study birational transformations phi : P-n -> <(phi(P-n))over bar> subset of P-N defined by linear systems of quadrics whose base locus is smooth and irreducible of dimension <= 3 and whose image <(phi(P-n))over bar... 
Quadratic form | Base locus | Birational transformation | MATHEMATICS | MATHEMATICS, APPLIED | HILBERT SCHEME | CREMONA TRANSFORMATIONS | quadratic form | GREATER-THAN | base locus | SYSTEMS | MANIFOLDS | EMBEDDED PROJECTIVE VARIETIES | Mathematics - Algebraic Geometry
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 4/2009, Volume 139, Issue 1, pp. 57 - 73
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve... 
Geometry | 14J26 | 14E07 | Birational transformation | Mathematics | Decomposition group | 14H50 | Inertia group | MATHEMATICS | MAPS | DECOMPOSITION | DYNAMICS | INERTIA | CREMONA GROUP | Mathematics - Algebraic Geometry
Journal Article
Rendiconti del Circolo Matematico di Palermo, ISSN 0009-725X, 12/2008, Volume 57, Issue 3, pp. 353 - 375
We study the relation between Cremona transformations in space and quadratic line complexes... 
Geometry | 14E07 | Algebra | 14N15 | Analysis | Cremona transformation | Mathematics, general | Mathematics | Applications of Mathematics | Quadratic line complex
Journal Article
Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 03/2007, Volume 83, Issue 3, pp. 21 - 26
Journal Article
Collectanea mathematica (Barcelona), ISSN 2038-4815, 2019, Volume 71, Issue 1, pp. 123 - 150
We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally... 
MATHEMATICS, APPLIED | 14E07 | CREMONA TRANSFORMATIONS | GREATER-THAN | VARIETIES | 14E05 | CATEGORIES | 14J30 | MATHEMATICS | DIMENSION | MANIFOLDS | ADJUNCTION | SURFACES | Mathematics - Algebraic Geometry
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2016, Volume 289, pp. 567 - 602
Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of Pr onto a prime Fano manifold such that the base locus X... 
Cremona transformations | Special birational transformations | Fano manifolds | Secondary | Primary | MATHEMATICS | ALGEBRAIC VARIETIES | MANIFOLDS | LOCUS | SURFACES | 3-FOLDS
Journal Article
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