Details:
Title | Numerical computation of the genus of an irreducible curve within an algebraic set | Author(s) | Daniel J. Bates, Chris Peterson, Andrew J. Sommese, Charles W. Wampler | Type | Article in Journal | Abstract | The common zero locus of a set of multivariate polynomials (with complex coefficients) determines an algebraic set. Any algebraic set can be decomposed into a union of irreducible components. Given a one-dimensional irreducible component, i.e. a curve, it is useful to understand its invariants. The most important invariants of a curve are the degree, the arithmetic genus and the geometric genus (where the geometric genus denotes the genus of a desingularization of the projective closure of the curve). This article presents a numerical algorithm to compute the geometric genus of any one-dimensional irreducible component of an algebraic set. | ISSN | 0022-4049 |
URL |
http://www.sciencedirect.com/science/article/pii/S0022404910002343 |
Language | English | Journal | Journal of Pure and Applied Algebra | Volume | 215 | Number | 8 | Pages | 1844 - 1851 | Year | 2011 | Edition | 0 | Translation |
No | Refereed |
No |
|