rationalCurve(d)
rationalCurve(d,D)
Computes the physical number of rational curves on a general complete intersection CalabiYau threefold in some projective space.
There are five types of such the complete intersections: quintic hypersurface in \mathbb P^4, complete intersections of types (4,2) and (3,3) in \mathbb P^5, complete intersection of type (3,2,2) in \mathbb P^6, complete intersection of type (2,2,2,2) in \mathbb P^7.
For lines:



This gives the numbers of lines on general complete intersection CalabiYau threefolds.
For conics:


The number of conics on a general quintic threefold can be computed as follows:

The numbers of conics on general complete intersection CalabiYau threefolds can be computed as follows:

For rational curves of degree 3:


The number of rational curves of degree 3 on a general quintic threefold can be computed as follows:

The numbers of rational curves of degree 3 on general complete intersection CalabiYau threefolds can be computed as follows:

For rational curves of degree 4:


The number of rational curves of degree 4 on a general quintic threefold can be computed as follows:

The numbers of rational curves of degree 4 on general complete intersections of types (4,2) and (3,3) in \mathbb P^5 can be computed as follows:


The object rationalCurve is a method function.