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.