Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Complete intersections in $ {\bf C}\sp{n}$ and $ R\sp{2n}$

Author: Marie A. Vitulli
Journal: Proc. Amer. Math. Soc. 78 (1980), 331-336
MSC: Primary 14G30; Secondary 14M10
MathSciNet review: 553370
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: When $ {{\mathbf{C}}^n}$ is identified with $ {{\mathbf{R}}^{2n}}$ in the usual way, algebraic varieties over the complex numbers give rise to varieties over the reals. We ask when a (strict) complete intersection in $ {{\mathbf{C}}^n}$ yields a (strict) complete intersection in $ {{\mathbf{R}}^{2n}}$. If the original variety V is connected, a necessary and sufficient condition that its image be a complete intersection is that V be irreducible. We give examples that show that without the connectedness assumption the conclusion is false.

In the course of proving this result we give an algebraic analogue of a result by Ephraim on germs of complex and the corresponding real analytic varieties. As our methods apply to varieties over the algebraic closure of an arbitrary real closed field the paper is written in this more general setting.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14G30, 14M10

Retrieve articles in all journals with MSC: 14G30, 14M10

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society