Polar Cremona transformations

By Igor Dolgachev. 2000

75 citations recorded by the source corpus.

is a birational map. We shall call F with such property a homaloidal polynomial. In this paper we review some known results about homaloidal polynomials and also classify them in the cases when F has no multiple factors and either n = 3 or n = 4 and F is the product of linear polynomials. I am grateful to Pavel Etingof, David Kazhdan, and Alexander Polishchuk for bringing to my attention the problem of classification of homaloidal polynomials and for various conversations on this matter. Also I thank Hal Schenck for making useful comments on my paper.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1d1cfca97082e791576e0a8f2e67b5468482e897

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Citations in the corpus

Cremona transformations and some related algebras (2004, unknown): “[4]).”
Classical Algebraic Geometry: A Modern View (2012, background): “Such a polynomial is called a homaloidal polynomial (see [181]).”
Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian (2007, background): “1 can be naturally extended to any dimension r 2, thus yielding an infinite series of homaloidal hypersurfaces in P , with r 2 (see [10]).”
Topics in classical algebraic geometry (2006, background): “Such a polynomial is called a homaloidal polynomial (see [92]).”
A characteristic-free criterion of birationality (2010, background): “The answer is positive in characteristic zero due to the theorem of Dolgachev [3].”