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TitleNumerical 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
TypeArticle in Journal
AbstractThe 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.
URL http://www.sciencedirect.com/science/article/pii/S0022404910002343
JournalJournal of Pure and Applied Algebra
Pages1844 - 1851
Translation No
Refereed No