Universidad Complutense de Madrid
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Real plane algebraic curves.

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Puente Muñoz, María Jesús de la (2002) Real plane algebraic curves. Expositiones Mathematicae, 20 (4). pp. 291-314. ISSN 0723-0869

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Official URL: http://www.sciencedirect.com/science/article/pii/S0723086902800093


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Abstract

We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi-definite nondefinite or definite. We present a discussion about isolated points. By means of the P operator, these points can be easily identified for curves defined by minimal polynomials of order bigger than one. We also discuss the conditions that a curve must satisfy in order to have a minimal polynomial. Finally, we list the most relevant topological properties of affine and projective, complex and real plane algebraic curves.


Item Type:Article
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21738
Deposited On:07 Jun 2013 14:17
Last Modified:12 Dec 2018 19:22

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