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Syzygies and Hilbert Functions

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Published by Chapman & Hall/CRC .
Written in English

Subjects:

  • Functional analysis,
  • Number Theory,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - General,
  • Combinatorics,
  • Mathematics / Number Theory,
  • Hilbert space,
  • Syzygies (Mathematics)

Book details:

Edition Notes

Lecture Notes in Pure and Applied Mathematics

The Physical Object
FormatPaperback
Number of Pages304
ID Numbers
Open LibraryOL8795552M
ISBN 101584888601
ISBN 109781584888604

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Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts. Written by international mathematics authorities, the book first examines the invariant of Castelnuovo-Mumford regularity, blowup algebras, and bigraded rings. of syzygies offers a microscope for enlarging our view of equations. This book is concerned with the qualitative geometric theory of syzygies: it describes some aspects of the geometry of a projective variety that cor-respond to the numbers and degrees of its syzygies or to its having some. The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts.A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging Brand: Springer.

The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research. 1. Hilbert Functions and Syzygies Counting functions that vanish on a set. Let K be a eld and let S= K[x0;;xr] be a ring of polynomials over K. If Xˆ Pr is a projective variety, the dimension of the space of forms (homogeneous polynomials) of each degree d vanishing on Xis an invariant of X, called the Hilbert function of the ideal IX File Size: KB. Hilbert’s insight was that it is determined by finitely many of its values. In many recent papers and books, Hilbert functions are studied using clever computations with binomials; we mention the binomial-approach briefly and avoid such computations whenever possible. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research Brand: Springer-Verlag London.

Discover Book Depository's huge selection of Irena Peeva books online. Free delivery worldwide on over 20 million titles. Stable Postulation and Stable Ideal Generation: Conjectures for Fat Points in the Plane Gimigliano, Alessandro, Harbourne, Brian, and Idà, Monica, Bulletin of the Belgian Mathematical Society - Simon Stevin, ; Approximating Common Fixed Points of Nonspreading-Type Mappings and Nonexpansive Mappings in a Hilbert Space Kim, Kyung Soo, Abstract and Applied Analysis, Cited by: There may then be a complicated range where h(d) continues to grow. But soon, certainly by the time d becomes n-1 or larger, everything becomes simple again as now h(d) stays constant at n. Both H and h are examples of Hilbert functions, a central concern of the book. The first issue is the behavior of h(d) in the complicated range. Here is our book, Computations in algebraic geometry with Macaulay 2, edited by David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd was published by Springer-Verlag in Septem , as number 8 in the series "Algorithms and Computations in Mathematics", ISBN , price DM 79,90 (net), or $