✦ LIBER ✦
Computing the minimal number of equations defining an affine curve ideal-theoretically
✍ Scribed by Hans Schoutens
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 107 KB
- Volume
- 177
- Category
- Article
- ISSN
- 0022-4049
No coin nor oath required. For personal study only.
✦ Synopsis
There is an algorithm which computes the minimal number of generators of the ideal of a reduced curve C in a ne n-space over an algebraically closed ÿeld K, provided C is not a local complete intersection.
The existence of such an algorithm follows from the fact that given d ∈ N, there exists d ∈ N, such that if a is a height n -1 radical ideal in K[X1; : : : ; Xn], generated by polynomials of degree at most d, then a admits a set of generators of minimal cardinality, with each generator having degree at most d , except possibly when K[X1; : : : ; Xn]=a is an (unmixed) local complete intersection.