Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach

Laurent Busé () and Marc Chardin ()
Additional contact information
Laurent Busé: Inria, Université Côte d’Azur
Marc Chardin: CNRS & Sorbonne Université, Institut de Mathématiques de Jussieu

A chapter in Commutative Algebra, 2021, pp 189-217 from Springer

Abstract: Abstract Parameterized algebraic curves and surfaces are widely used in geometric modeling and their manipulation is an important task in the processing of geometric models. In particular, the determination of the intersection loci between points, pieces of parameterized algebraic curves and pieces of algebraic surfaces is a key problem in this context. In this paper, we survey recent methods based on syzygies and blowup algebras for computing the image and the finite fibers of a curve or surface parameterization, more generally of a rational map. Conceptually, the main idea is to use elimination matrices, mainly built from syzygies, as representations of rational maps and to extract geometric informations from them. The construction and main properties of these matrices are first reviewed and then illustrated through several settings, each of them highlighting a particular feature of this approach that combines tools from commutative algebra, algebraic geometry and elimination theory.

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_6

Ordering information: This item can be ordered from
http://www.springer.com/9783030896942

DOI: 10.1007/978-3-030-89694-2_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().