I read about your intentions and agendas in order to ensure smooth completion of the conference.

Nonetheless, the affine curve can be embedded in a unique compact Riemann surface called its smooth completion.

This smooth completion can also be obtained as follows.

A smooth connected curve over an algebraically closed field is called hyperbolic if where g is the genus of the smooth completion and r is the number of added points.

By construction, the smooth completion is a projective curve which contains the given curve as an everywhere dense open subset, and the added new points are smooth.

If the base field is not perfect, a smooth completion of a smooth affine curve doesn't always exist.

If X is quasi-projective, the smooth completion can be chosen to be projective.

However, contrary to the one-dimensional case, there is no uniqueness of the smooth completion, nor is it canonical.

The problem of resolution of singularities is to know if every algebraic variety is birationally equivalent to a variety whose projective completion is nonsingular (see also smooth completion).

Almost imperceptibly, they paired off and sank down together only to stand again, one man turning away to leave the other in a smooth completion of the dance phrase.