Asymptotes of space curves

In Blasco and Perez-Diaz (2014) (see 3), a method for computing generalized asymptotes of a real algebraic plane curve implicitly defined is presented. Generalized asymptotes are curves that describe the status of a branch at points with sufficiently large coordinates and thus, it is an important tool to analyze the behavior at infinity of an algebraic curve. This motivates that in this paper, we analyze and compute the generalized asymptotes of a real algebraic space curve which could be parametrically or implicitly defined. We present an algorithm that is based on the computation of the infinity branches (this concept was already introduced for plane curves in Blasco and Perez-Diaz (2014) 1). In particular, we show that the computation of infinity branches in the space can be reduced to the computation of infinity branches in the plane and thus, the methods in Blasco and Perez-Diaz (2014) (see 1) can be applied.

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