Determinantal Ideals

  • Rosa M. Miró-Roig
Part of the Progress in Mathematics book series (PM, volume 264)

About this book

Introduction

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.

Keywords

Combinatorics Representation theory algebraic geometry commutative algebra determinantal ideal liaison class

Authors and affiliations

  • Rosa M. Miró-Roig
    • 1
  1. 1.Departement d’Algebra i Geometria Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8535-4
  • Copyright Information Birkhäuser Verlag AG 2008
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8534-7
  • Online ISBN 978-3-7643-8535-4