• Publications
  • Influence
Commutative Algebra: with a View Toward Algebraic Geometry
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents aExpand
Three-Dimensional Link Theory and Invariants of Plane Curve Singularities.
This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic constructionExpand
Homological algebra on a complete intersection, with an application to group representations
Let R be a regular local ring, and let A = R/(x), where x is any nonunit of R. We prove that every minimal free resolution of a finitely generated A -module becomes periodic of period 1 or 2 after atExpand
Binomial Ideals
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains manyExpand
Limit linear series: Basic theory
AbstractIn this paper we introduce techniques for handling the degeneration of linear series on smooth curves as the curves degenerate to a certain type of reducible curves, curves of compact type.Expand
Linear Free Resolutions and Minimal Multiplicity
Let S = k[x, ,..., x,] be a polynomial ring over a field and let A4 = @,*-a, M, be a finitely generated graded module; in the most interesting case A4 is an ideal of S. For a given natural number p,Expand
The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry
Preface: Algebra and Geometry * Free Resolutions and Hilbert Functions * First Examples of Free Resolutions * Points in P^2 * Castelnuovo-Mumford Regularity * The Regularity of Projective Curves *Expand
The Geometry Of Schemes
1 Basic Definitions 2 Examples 3 Projective Schemes 4 Classical Constructions 5 Local Constructions 6 Schemes and Functors