Determinantal Ideals

Front Cover
Springer Science & Business Media, Dec 31, 2007 - Mathematics - 140 pages
0 Reviews

Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls.

Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals.

Winner of the Ferran Sunyer i Balaguer Prize 2007.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

Background
1
12 Determinantal ideals
13
13 CIliaison and Gliaison
21
CIliaison and Gliaison of Standard Determinantal Ideals
29
21 CIliaison class of CohenMacaulay codimension 2 ideals
30
22 CIliaison class of standard determinantal ideals
33
23 Gliaison class of standard determinantal ideals
41
Multiplicity Conjecture for Standard Determinantal Ideals
45
Unobstructedness and Dimension of Families of Standard Determinantal Ideals
62
41 Families of codimension 2 CohenMacaulay algebras
65
42 Unobstructedness and dimension of families of determinantal schemes
67
Determinantal Ideals Symmetric Determinantal Ideals and Open Problems
105
51 Liaison class of determinantal and symmetric determinantal ideals
106
52 The multiplicity conjecture for determinantal and symmetric determinantal ideals
111
53 Unobstructedness and dimension of families of determinantal and symmetric determinantal ideals
119
Bibliography
129

31 The multiplicity conjecture for CohenMacaulay codimension 2 ideals
47
32 The multiplicity conjecture for standard determinantal ideals
50

Other editions - View all

Common terms and phrases

Popular passages

Page vii - Sunyer i Balaguer (1912-1967) was a selftaught Catalan mathematician who, in spite of a serious physical disability, was very active in research in classical mathematical analysis, an area in which he acquired international recognition. His heirs created the Fundacio Ferran Sunyer i Balaguer inside the Institut d'Estudis Catalans to honor the memory of Ferran Sunyer i Balaguer and to promote mathematical research. Each year, the Fundacio Ferran Sunyer i Balaguer and the Institut d'Estudis Catalans...
Page vii - Antonio Cordoba Universidad Autonoma de Madrid Paul Malliavin Universite de Paris VI Joseph Oesterle Universite de Paris VI Oriol Serra Universitat Politecnica de Catalunya, Barcelona Alan Weinstein University of California at Berkeley MCMVII" Ferran Sunyer i Balaguer Prize winners since 1997: 1997 Albrecht Bottcher and Yuri I.
Page viii - Systems, PM 179 1999 Patrick Dehornoy Braids and Self-Distributivity, PM 192 2000 Juan-Pablo Ortega and Tudor Ratiu Hamiltonian Singular Reduction, PM 222 2001 Martin Golubitsky and Ian Stewart The Symmetry Perspective, PM 200 2002 Andre Unterberger Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi, PM 209 Alexander Lubotzky and Dan Segal Subgroup Growth, PM 212 2003 Fuensanta Andreu-Vaillo, Vincent Caselles and Jose M. Mazon Parabolic Quasilinear Equations Minimizing Linear Growth...
Page viii - ... Vincent Caselles and Jose M. Mazon Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, PM 223 2004 Guy David Singular Sets of Minimizers for the Mumford-Shah Functional, PM 233 2005 Antonio Ambrosetti and Andrea Malchiodi Perturbation Methods and Semilinear Elliptic Problems on Rn, PM 240 Jose Seade On the Topology of Isolated Singularities in Analytic Spaces, PM 241 2006 Xiaonan Ma and George Marinescu Holomorphic Morse Inequalities and Bergman Kernels, PM 254 To Pere and Rosa...
Page viii - PM 200 2002 Andre Unterberger Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi, PM 209 Alexander Lubotzky and Dan Segal Subgroup Growth, PM 212 2003 Fuensanta Andreu-Vaillo, Vincent Caselles and Jose M. Mazon Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, PM 223 2004 Guy David Singular Sets of Minimizers for the Mumford-Shah Functional, PM 233 2005 Antonio Ambrosetti and Andrea Malchiodi Perturbation Methods and Semilinear Elliptic Problems on R", PM 240...

Bibliographic information