On Cremona transformations of \(\mathbb{P}^3\) with all possible bidegrees
type: Item
instance of: scholarly article
title: On Cremona transformations of \(\mathbb{P}^3\) with all possible bidegrees
zbMATH Open document ID: 1278.14018
author: Iván Pan
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2013-09-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.2038
full work available at URL: S1631073X13001362
review text: A Cremona map \(F:\mathbb P^3\dashrightarrow\mathbb P^3\) has bidegree \((d,e)\) if \(F\) is defined by homogeneous polynomials of degree \(d\) and \(F^{-1}\) by homogeneous polynomials of degree \(e\). The author proves the existence of such maps for all bidegrees \((d,e)\) with \(d, e\geq 2\) and \(\sqrt{d}\leq e\leq d^2\). This corrects a mistake in [C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 4, 297--300 (2000; Zbl 1011.14003)]. Explicit constructions are given.
reviewed by: Emilia Mezzetti
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 6211815
zbMATH Keywords: Cremona transformation
zbMATH Keywords: birational map
MaRDI profile type: Publication
OpenAlex ID: W1999251444
arXiv ID: 1304.2038
cites work: Geometry of the plane Cremona maps
cites work: Les transformations de Cremona stellaires. (The stellar Cremona transformations)
cites work: Sur le multidegré des transformations de Cremona
DOI: 10.1016/J.CRMA.2013.06.003
description: scientific article; zbMATH DE number 6211815