Determinantal Ideals

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.

List of contents

Background.- CI-liaison and G-liaison of Standard Determinantal Ideals.- Multiplicity Conjecture for Standard Determinantal Ideals.- Unobstructedness and Dimension of Families of Standard Determinantal Ideals.- Determinantal Ideals, Symmetric Determinantal Ideals, and Open Problems.

Summary

Determinantal ideals are a central topic in both commutative algebra and algebraic geometry. In this book, three problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; unobstructedness and dimension of families of standard determinantal ideals. Winner of the Ferran Sunyer i Balaguer Prize 2007.

Product details

• Authors: Rosa M Miró-Roig, Rosa M. Miró-Roig, Rosa M. Miró-Roig
• Publisher: Springer, Basel
• Languages: English
• Product format: Hardback
• Released: 20.11.2007
• EAN: 9783764385347
• ISBN: 978-3-7643-8534-7
• No. of pages: 140
• Dimensions: 155 mm x 12 mm x 235 mm
• Weight: 356 g
• Illustrations: XVI, 140 p.
• Series: Progress in Mathematics; Progress in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, Diskrete Mathematik, Combinatorics, Mathematics and Statistics, Discrete Mathematics, Combinatorics & graph theory, Commutative algebra, Commutative rings, Commutative Rings and Algebras