ag.algebraic geometry - Algorithms for semistable reduction of families of curves

If your curves are in P^n (specifically in P^2 - as in your example), I think there is something you can do: project your curves from a general P^{n-2} to P^1. This means that you
are now looking for a limit in a Hurwitz scheme. This can be broken into two problems:

• looking for the limit on the underlying M_{0,n}




• tracing the ramification structure.

Here is an example: find the limit of F+t Q^2 where F is a plane quartic, and Q is a plane quadric.

Project from your favorite random point. You can verify that the limit of the ramification points on the family are

From here you can continue in a variety of ways (e.g. you have a pencil of g^1_4 s on the limit curve which break through a map from the limit curve to a plane conic, which has 8 ramification points)