David A. Cox

2. The Geometry of Elimination (2009)

David A. Cox

Gröbner bases were introduced in Bucherger’s thesis [2] and developed further in [1, 3]. These methods are now featured in textbooks such [6, 7] and have been implemented in most computer algebra...

Primitive Collections and Toric Varieties (2008)

Cox, David A., Von Renesse, Christine

This paper studies Batyrev's notion of primitive collection. We use primitive collections to characterize the nef cone of a quasi-projective toric variety whose fan has convex support, a result...

MATHÉMATIQUES What is the Role of Algebra in Applied Mathematics? (2008)

David A. Cox, D. A. Cox

When I first encountered abstract algebra in the late 1960s, I was drawn to its power and beauty. One of the liberating ideas of the subject is that in dealing with algebraic structures, you don’t...

École d’Été CIMPA Systèmes d’équations polynomiales: de la géométrie algébrique aux applications industrielles. Près de Buenos Aires, Argentine. (2008)

David A. Cox, Alicia Dickenstein, Lorenzo Robbiano (univ, Ioannis Emiris

Genova) Eigenvalue and eigenvector methods for solving polynomial equations Introduction to residues and resultants Polynomial systems and some applications to statistics

Impact of multivessel disease on reperfusion success and clinical outcomes in patients undergoing primary percutaneous coronary intervention for acute myocardial infarction (2007)

Sorajja, Paul, Gersh, Bernard J., Cox, David A., McLaughlin, Michael G., Zimetbaum, Peter, Costantini, Costantino, ...

Aims We sought to investigate the impact of multivessel coronary artery disease (CAD) on reperfusion success and prognosis following primary percutaneous coronary intervention (PCI) in patients with...

Bivalirudin for patients with acute coronary syndromes (2006)

McLaurin, Brent T, Cox, David A, Bertrand, Michel E, Lincoff, A Michael, Moses, Jeffrey W, ...

BACKGROUND: Current guidelines for patients with moderate- or high-risk acute coronary syndromes recommend an early invasive approach with concomitant antithrombotic therapy, including aspirin,...

Bezoutians and Tate Resolutions (2006)

Cox, David A.

This paper gives an explicit construction of the Tate resolution of sheaves arising from the d-fold Veronese embedding of P^n. Our description involves the Bezoutian of n+1 homogenous forms of degree...

Platelet glycoprotein IIb/IIIa receptor inhibition as adjunctive treatment during saphenous vein graft stenting: differential effects after randomization to occlusion or filter-based embolic protection (2006)

Jonas, Michael, Stone, Gregg W., Mehran, Roxana, Hermiller, James, Feldman, Robert, Herrmann, Howard C., ...

Aims Although embolic protection devices reduce complications during saphenous vein graft (SVG) stenting, adverse events still occur in ∼10% of patients. IIb/IIIa antagonists have not been...

Platelet glycoprotein IIb/IIIa receptor inhibition as adjunctive treatment during saphenous vein graft stenting: differential effects after randomization to occlusion or filter-based embolic protection (2006)

Jonas, Michael, Stone, Gregg W., Mehran, Roxana, Hermiller, James, Feldman, Robert, Herrmann, Howard C., ...

Aims Although embolic protection devices reduce complications during saphenous vein graft (SVG) stenting, adverse events still occur in ∼10% of patients. IIb/IIIa antagonists have not been proven...

Combined prognostic utility of ST-segment recovery and myocardial blush after primary percutaneous coronary intervention in acute myocardial infarction (2005)

Sorajja, Paul, Gersh, Bernard J., Costantini, Costantino, McLaughlin, Michael G., Zimetbaum, Peter, Cox, David A., ...

Aims ST-segment recovery (ΣSTR) and myocardial blush (MB) evaluate different elements of microcirculatory integrity after reperfusion therapy in acute myocardial infarction (AMI). We sought to...

Combined prognostic utility of ST-segment recovery and myocardial blush after primary percutaneous coronary intervention in acute myocardial infarction (2005)

Sorajja, Paul, Gersh, Bernard J., Costantini, Costantino, McLaughlin, Michael G., Zimetbaum, Peter, Cox, David A., ...

Aims ST-segment recovery (ΣSTR) and myocardial blush (MB) evaluate different elements of microcirculatory integrity after reperfusion therapy in acute myocardial infarction (AMI). We sought to...

Implicitizing rational surfaces with base points using the method of moving surfaces (2003)

Jiannmin Zheng, Thomas W. Sederberg, Eng-wee Chionh, David A. Cox

Abstract. 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...

Equations of Parametric Surfaces via Syzygies (2000)

Cox, David A.

The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula...

Virtual Fundamental Classes of Zero Loci (2000)

Cox, David A., Katz, Sheldon, Lee, Yuan-Pin

Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a...

Recent developments in toric geometry (1996)

Cox, David A.

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric...

Toric Residues (1994)

Cox, David A.

In ${\bf C}^{n+1}$, one can show that the residue of $n+1$ homogeneous forms of the same degree equals the integral of a certain $(n,n)$ form over ${\bf P}^n$. Furthermore, the Jacobian of the forms...

The Functor of a Smooth Toric Variety (1993)

Cox, David A.

A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In this paper, we generalize this description to the case of maps from Y to an arbitrary smooth toric variety. The data needed...

On the Hodge Structure of Projective Hypersurfaces in Toric Varieties (1993)

Batyrev, Victor V., Cox, David A.

This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric...

The Homogeneous Coordinate Ring of a Toric Variety, Revised Version (1992)

Cox, David A.

This revised version is somewhat shorter than the original. It also mentions the other people who have discovered independently the construction (or closely related constructions) of toric varieties...

Toric Varieties and Toric Resolutions

David A. Cox

This paper is an introduction to toric varieties and toric resolutions. We begin with basic denitions and examples, and then cover standard topics in toric geometry, including fans, support...