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 onedimensional 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 onedimensional irreducible component of an algebraic set.  ISSN  00224049 
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 
