All Items 4

The story of ideals, varieties and algorithms

Cox, David A. (Department of Mathematics and Statistics, Amherst College)

This expository article tells the story of how the book "Ideals, Varieties and Algorithms" came to be written.

The homogeneous coordinate ring of a toric variety

Cox, David A. (Department of Mathematics and Statistics, Amherst College)

The original version of a paper, published in 1995. The paper introduced the homogeneous coordinate ring of a toric variety (now called the total coordinate ring or Cox ring) and gave a quotient construction. The paper also studied sheaves on a toric variety, and in Section 4 described its automorphism group.

Strata of rational space curves

Cox, David A. (Department of Mathematics and Statistics, Amherst College)

The μ-invariant image of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same μ-type, what we call a μ-stratum, and as well the closure of strata. Many of our results are based on papers by the second author that appeared in the commutative algebra literature. We also present new results, including an explicit formula for the codimension of the locus of non-proper parametrizations within each μ-stratum and a decomposition of the smallest μ-stratum based on which two-dimensional rational normal scroll the curve lies on.

The homogeneous coordinate ring of a toric variety [Erratum]

Cox, David A. (Department of Mathematics and Statistics, Amherst College)

An erratum that corrects an error in the proof of Proposition 4.3 in the paper "The Homogeneous Coordinate Ring of a Toric Variety." The error in the proof of Proposition 4.3 resulted from the faulty assumption that a certain set of graded endomorphisms forms a ring; rather, it is a monoid under composition. The erratum notes this error and gives a correct proof of the proposition.