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Birkhäuser - Birkhäuser Mathematics | Determinantal Ideals

Determinantal Ideals

Series: Progress in Mathematics, Vol. 264

Miró-Roig, Rosa M.

2008, XVI, 140 p.

A product of Birkhäuser Basel
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  • Winner of the Ferran Sunyer i Balaguer Prize 2007
  • Gives new insights in open problems in liaison theory and Hilbert schemes
  • Publishes new results on determinantal ideals and gives an overview of recent developments

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.

Content Level » Research

Keywords » Combinatorics - Representation theory - algebraic geometry - commutative algebra - determinantal ideal - liaison class

Related subjects » Birkhäuser Mathematics

Table of contents / Preface 

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