A characteristic-free criterion of birationality

DOI10.1016/j.aim.2011.12.005zbMath1251.14007arXiv1101.0197OpenAlexW2011201737MaRDI QIDQ411738

A. V. Doria, Seyed Hamid Hassanzadeh, Aaron Simis

Publication date: 30 April 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.0197

zbMATH Keywords

rational mapembedding dimensionbase idealbirationality criterionCremona mapJacobian dual rank

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Birational automorphisms, Cremona group and generalizations (14E07) Rational and birational maps (14E05)

Related Items (36)

Companion varieties for root systems and Fermat arrangements ⋮ Tri-linear birational maps in dimension three ⋮ Computations with rational maps between multi-projective varieties ⋮ Degenerations of the generic square matrix, the polar map and the determinantal structure ⋮ Linearly presented perfect ideals of codimension 2 in three variables ⋮ Extremal Rees algebras ⋮ Degree of rational maps versus syzygies ⋮ De Jonquières transformations in arbitrary dimension. An ideal theoretic view ⋮ Multiplicity of the saturated special fiber ring of height three Gorenstein ideals ⋮ Homaloidal nets and ideals of fat points II: Subhomaloidal nets ⋮ Symbolic powers of perfect ideals of codimension 2 and birational maps ⋮ Implicitization of de Jonquières parametrizations ⋮ RationalMaps, a package for Macaulay2 ⋮ The isomorphism problem of projective schemes and related algorithmic problems ⋮ A study of nonlinear multiview varieties ⋮ Tight and adjusted equigenerated sequences, and the special fiber ⋮ Homaloidal determinants ⋮ Plane Cremona maps: saturation and regularity of the base ideal ⋮ BLOWUPS AND FIBERS OF MORPHISMS ⋮ Symmetry preserving degenerations of the generic symmetric matrix ⋮ Equations defining certain graphs ⋮ Cremona maps defined by monomials ⋮ Plane polar Cremona maps of arbitrarily large degree in positive characteristic ⋮ Effective criteria for bigraded birational maps ⋮ Bounds on degrees of birational maps with arithmetically Cohen-Macaulay graphs ⋮ A blowup algebra for hyperplane arrangements ⋮ On catalecticant perfect ideals of codimension 2 ⋮ A theorem about Cremona maps and symbolic Rees algebras ⋮ Homology of homogeneous divisors ⋮ Multiplicity of the saturated special fiber ring of height two perfect ideals ⋮ The ubiquity of Sylvester forms in almost complete intersections ⋮ Homaloidal nets and ideals of fat points I ⋮ Blowup algebras of rational normal scrolls ⋮ On ideals generated by \(a\)-fold products of linear forms ⋮ Coordinate sections of generic Hankel matrices ⋮ Rational maps of ℙⁿ with prescribed fixed points and the smooth conic case

Uses Software

• Macaulay2
• RationalMaps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear syzygies and birational combinatorics
• Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
• Cremona transformations and syzygies
• Cremona transformations and some related algebras
• Cremona transformations and special double structures
• Codimension, multiplicity and integral extensions
• Combinatorics of Cremona monomial maps
• The Syzygies of the Conormal Module
• Rees Algebras of Modules
• Constraints for the normality of monomial subrings and birationality
• Jacobian Dual Fibrations
• Polar Cremona transformations.

This page was built for publication: A characteristic-free criterion of birationality