Rosa M. Miró-Roig (auth.)3764385340, 978-3-7643-8534-7
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.
Table of contents :
Front Matter….Pages i-xvi
Background….Pages 1-28
CI-liaison and G-liaison of Standard Determinantal Ideals….Pages 29-43
Multiplicity Conjecture for Standard Determinantal Ideals….Pages 45-61
Unobstructedness and Dimension of Families of Standard Determinantal Ideals….Pages 63-103
Determinantal Ideals, Symmetric Determinantal Ideals, and Open Problems….Pages 105-128
Back Matter….Pages 129-138
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