algebraic curve

(redirected from Rational curve)
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algebraic curve

[¦al·jə¦brā·ik ′kərv]
(mathematics)
The set of points in the plane satisfying a polynomial equation in two variables.
More generally, the set of points in n-space satisfying a polynomial equation in n variables.
References in periodicals archive ?
Now consider the log surface (X, D') where D0 is the image of the smooth rational curve D.
containing no rational curve of degree [less than or equal to] 16 (not even singular ones).
The following items are arranged (in columns): dataset examined, the type of curve reconstructed (NR: nonrational; R: rational), the schema executed for rational curves (AIO: all-in-one; SEQ: sequential), the total number of calls to the energy function in the best case (represented by [n.
i) The points drawing the curvature centers of the pole trajectories form a third order rational curve at time t in the moving plane E .
Automatic Parameterization of Rational Curves and Surfaces IV: Algebraic Space Curves
Each one of them has a cycle formed by n rational curves [C.
Suppose that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a flag curve corresponding to a g-stable rational curve [R, [x.
i] be a family of rational curves on X containing [[GAMMA].
We recall that an exceptional curve is a smooth rational curve C such that [C.
5] contains no rational curve of degree d, for 2 [less than or equal to] d [less than or equal to] 15.
X] + [DELTA])-negative rational curve on X whenever [K.
In the case n = 2 the solution to the problem is predicted by the equivalent conjectures of Segre, Harbourne, Gimigliano and Hirschowitz [17, 10, 9, 12], hereafter "SHGH conjecture", that can be formulated in the following way: the divisor D is special if and only if there exists a rational curve C whose normal bundle is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and such that D x C [less than or equal to] -2.

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