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Algebra, Geometry and Their Interactions
Edited by: Alberto Corso, University of Kentucky, Lexington, KY, and Juan Migliore and Claudia Polini, University of Notre Dame, IN

Contemporary Mathematics
2007; 270 pp; softcover
Volume: 448
ISBN-10: 0-8218-4094-0
ISBN-13: 978-0-8218-4094-8
List Price: US$86
Member Price: US$68.80
Order Code: CONM/448
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This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.


Graduate students and research mathematicians interested in communitative algebra and algebraic geometry.

Table of Contents

  • M. Bertolini, G. M. Besana, and C. Turrini -- Instability of projective reconstruction from 1-view near critical configurations in higher dimensions
  • K. A. Chandler -- Examples and counterexamples on the conjectured Hilbert function of multiple points
  • C. Ciuperca, W. Heinzer, J. Ratliff, and D. Rush -- Projectively full ideals in Noetherian rings, a survey
  • K. Dalili and W. V. Vasconcelos -- Cohomological degrees and the HomAB conjecture
  • J. A. Eagon -- A minimal generating set for the first syzygies of a monomial ideal
  • E. Gorla -- Lifting the determinantal property
  • H. T. Há and A. Van Tuyl -- Resolutions of square-free monomial ideals via facet ideals: A survey
  • M. Hochster -- Some finiteness properties of Lyubeznik's \(\mathcal{F}\)-modules
  • C. Huneke, J. Migliore, U. Nagel, and B. Ulrich -- Minimal homogeneous liaison and Licci ideals
  • J. O. Kleppe and R. M. Miró-Roig -- Unobstructedness and dimension of families of codimension 3 ACM algebras
  • A. Lanteri and H. Maeda -- Ample vector bundles with sections vanishing on submanifolds of sectional genus three
  • Y. Lu, D. J. Bates, A. J. Sommese, and C. W. Wampler -- Finding all real points of a complex curve
  • R. M. Miró-Roig -- On the multiplicity conjecture
  • J. M. Rojas -- Efficiently detecting torsion points and subtori
  • A. K. Singh and S. Spiroff -- Divisor class groups of graded hypersurfaces
  • K. E. Smith and H. M. Thompson -- Irrelevent exceptional divisors for curves on a smooth surface
  • M. A. van Opstall and R. Veliche -- Variation of hyperplane sections
  • C. Yuen -- Jet schemes of determinantal varieties
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