Syzygies and Hilbert Functions

Syzygies and Hilbert Functions

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Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. 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. It then outlines the current status of two challenging conjectures: the lex-plus-power (LPP) conjecture and the multiplicity conjecture. After reviewing results of the geometry of Hilbert functions, the book considers minimal free resolutions of integral subschemes and of equidimensional Cohen-Macaulay subschemes of small degree. It also discusses relations to subspace arrangements and the properties of the infinite graded minimal free resolution of the ground field over a projective toric ring. The volume closes with an introduction to multigraded Hilbert functions, mixed multiplicities, and joint reductions. By surveying exciting topics of vibrant current research, Syzygies and Hilbert Functions stimulates further study in this hot area of mathematical more

Product details

  • Paperback | 304 pages
  • 154.9 x 228.6 x 22.9mm | 317.52g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 6 black & white illustrations, 7 black & white tables
  • 1584888601
  • 9781584888604

About Irena Peeva

Cornell University, Ithaca, New Yorkshow more

Table of contents

Some Results and Questions on Castelnuovo-Mumford Regularity Marc Chardin Hilbert Coefficients of Ideals with a View toward Blowup Algebras Alberto Corso and Claudia Polini A Case Study in Bigraded Commutative Algebra David Cox, Alicia Dickenstein and Hal Schenck Lex-Plus-Powers Ideals Christopher A. Francisco and Benjamin P. Richert Multiplicity Conjectures Christopher A. Francisco and Hema Srinivasan The Geometry of Hilbert Functions Juan C. Migliore Minimal Free Resolutions of Projective Subschemes of Small Degree Uwe Nagel Infinite Free Resolutions over Toric Rings Irena Peeva Resolutions and Subspace Arrangements Jessica Sidman Multigraded Hilbert Functions and Mixed Multiplicities Irena Swanson Indexshow more