Numerical computation of the genus of an irreducible curve within an algebraic set

被引：6

作者：

Bates, Daniel J. ^{[1
]}

Peterson, Chris ^{[1
]}

Sommese, Andrew J. ^{[2
]}

Wampler, Charles W. ^{[3
]}

机构：

[1] Colorado State Univ, Dept Math, Ft Collins, CO 80525 USA

[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[3] Gen Motors Res & Dev, Warren, MI 48090 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2011年 / 215卷 / 08期

关键词：

COMPUTING SINGULAR SOLUTIONS; BEZOUT-THEOREM; COMPLEXITY; SYSTEMS;

D O I：

10.1016/j.jpaa.2010.10.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1844 / 1851

页数：8

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