Our discussion applies to Maple 13. For us, the most important part of Maple is the Groebner package, though there is also the PolynomialIdeals package that will be discussed later in the section. To have access to the commands in the Groebner package, type: > with(Groebner) (here, > is the Maple prompt). Once the Groebner package is loaded, you can perform… (More)
This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each one-dimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group A n−1 (X) of X (where n = dim X). Using this graded ring, we will… (More)
General Information Since the second edition of Using Algebraic Geometry appeared in 2005, Maple's Groebner package has undergone further revisions and extensions. Hence some of the discussion in the text and some examples are no longer up-to-date. The purposes of this update are to indicate the most important changes, to illustrate some of the increased… (More)
The purpose of this paper is to explain one extension of the ideas of the Griffiths-Dolgachev-Steenbrink method for describing the Hodge theory of smooth (resp. quasi-smooth) hypersurfaces in complex projective spaces (resp. in weighted projective spaces).
This errata sheet is organized by which printing of the book you have. The printing can be found by looking at the string of digits 10 9 8. .. at the bottom of the copyright page: the last digit that appears in this decreasing string indicates the printing.
The method of moving planes and moving quadrics can express the implicit equation of a parametric surface as the determinant of a matrix M. The rows of M correspond to moving planes or moving quadrics that follow the parametric surface. Previous papers on the method of moving surfaces have shown that a simple base point has the effect of converting one… (More)
These are notes for a lecture given at Ohio University on June 3, 2006. An important topic in commutative algebra is the Rees algebra of an ideal in a commutative ring. The Rees algebra encodes a lot of information about the ideal and corresponds geometrically to a blow-up. One can represent the Rees algebra as the quotient of a polynomial ring by an ideal.… (More)
Techniques from algebraic geometry and commutative algebra are adopted to establish suucient polynomial conditions for the validity of implicitization by the method of moving quadrics both for rectangular tensor product surfaces of bi-degree (m; n) and for triangular surfaces of total degree n in the absence of base points.