Classification of Algebraic Space Curves, III

1994 ◽  
pp. 113-120 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
Algebraic Space ◽  
Space Curves

scholarly journals Parallel Software to Offset the Cost of Higher Precision

2021 ◽  
Vol 40 (2) ◽  
pp. 59-64
Author(s):  
Jan Verschelde
Keyword(s):  
Power Series ◽  
Parallel Algorithms ◽  
Series Expansions ◽  
Use Case ◽  
Double Precision ◽  
Algebraic Space ◽  
Space Curves ◽  
Computational Overhead ◽  
Power Series Expansions ◽  
The Cost

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.

Integral closure of some co-ordinate rings

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.

scholarly journals Intersection of algebraic space curves

1991 ◽  
Vol 31 (2) ◽  
pp. 81-96 ◽  
Author(s):  
Shreeram S. Abhyankar ◽  
Srinivasan Chandrasekar ◽  
Vijaya Chandru
Keyword(s):  
Algebraic Space ◽  
Space Curves
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