The Homogeneous coordinate ring of a toric variety, revised version

Abstract

This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper Homogeneous Coordinate Ring of a Toric Variety, and 2) the original (unchanged) version of the paper, published in 1995. The original 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. 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.