The moving curve ideal and the Rees algebra

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. This ideal is generated by the defining relations of the Rees algebra. The surprise is that these defining relations were discovered by computer scientists working in computer-aided geometric design, where the ideal is called the moving curve ideal. A second surprise will be the appearance of adjoint curves.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: David A. Cox
• Keywords: Commutative Algebra, Ideal, Rees Algebra, TCS 2008, Theoretical Computer Science