© 2016

Minimal Free Resolutions over Complete Intersections


Part of the Lecture Notes in Mathematics book series (LNM, volume 2152)

Table of contents

  1. Front Matter
    Pages i-x
  2. David Eisenbud, Irena Peeva
    Pages 1-17
  3. David Eisenbud, Irena Peeva
    Pages 19-21
  4. David Eisenbud, Irena Peeva
    Pages 23-35
  5. David Eisenbud, Irena Peeva
    Pages 37-48
  6. David Eisenbud, Irena Peeva
    Pages 49-62
  7. David Eisenbud, Irena Peeva
    Pages 63-83
  8. David Eisenbud, Irena Peeva
    Pages 85-93
  9. David Eisenbud, Irena Peeva
    Pages 95-101
  10. Back Matter
    Pages 103-110

About this book


This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957.

The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.


13D02, 11-XX Free Resolutions Matrix Factorizations Complete Intersections, Betti Numbers Syzygies

Authors and affiliations

  1. 1.University of CaliforniaMSRI & Mathematics DepartmentBerkeleyUSA
  2. 2.Mathematics DepartmentCornell UniversityIthacaUSA

Bibliographic information


“The text provides a wonderful introduction describing the background which led to the development of higher matrix factorizations and includes (with proofs and examples) all the theory required to understand the new material and put it in context.” (Benjamin P. Richert, Mathematical Reviews, May, 2017)