Automatic parameterization of rational curves and surfaces IV: algebraic space curves

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates for this overhead. Newton's method to develop power series expansions of algebraic space curves is the use case for this application.

Download Full-text

On the Classification of Algebraic Space Curves

Vector Bundles and Differential Equations ◽

10.1007/978-1-4684-9415-0_5 ◽

1980 ◽

pp. 83-112 ◽

Cited By ~ 15

Author(s):

Robin Hartshorne

Keyword(s):

Algebraic Space ◽

Space Curves

Download Full-text

Smoothing algebraic space curves

Lecture Notes in Mathematics - Algebraic Geometry Sitges (Barcelona) 1983 ◽

10.1007/bfb0074998 ◽

1985 ◽

pp. 98-131 ◽

Cited By ~ 34

Author(s):

R. Hartshorne ◽

A. Hirschowitz

Keyword(s):

Algebraic Space ◽

Space Curves

Download Full-text

RATIONAL CURVES AND SURFACES: ALGORITHMS AND SOME APPLICATIONS

Lecture Notes Series on Computing - Geometric Computation ◽

10.1142/9789812794833_0003 ◽

2004 ◽

pp. 65-125

Author(s):

J. Rafael Sendra

Keyword(s):

Rational Curves ◽

Curves And Surfaces

Download Full-text

Integral closure of some co-ordinate rings

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700023995 ◽

1975 ◽

Vol 20 (1) ◽

pp. 115-123

Author(s):

David J. Smith

Keyword(s):

Integral Closure ◽

Principal Result ◽

Space Curve ◽

Coordinate Ring ◽

Unique Factorization ◽

Algebraic Space ◽

Space Curves ◽

Integrally Closed ◽

Coordinate Rings ◽

Special Case

In this paper, some methods are developed for obtaining explicitly a basis for the integral closure of a class of coordinate rings of algebraic space curves.The investigation of this problem was motivated by a need for examples of integrally closed rings with specified subrings with a view toward examining questions of unique factorization in them. The principal result, giving the elements to be adjoined to a ring of the form k[x1, …,xn] to obtain its integral closure, is limited to the rather special case of the coordinate ring of a space curve all of whose singularities are normal. But in numerous examples where the curve has nonnormal singularities, the same method, which is essentially a modification of the method of locally quadratic transformations, also gives the integral closure.

Download Full-text