| Two problems concerning rational curves on K3 surfaces will be studied in this paper. The first problem is the existence of rational curves on an algebraic K3 surface. We are able to generalize the existence theorem of S. Mori and S. Mukai to the existence of rational curves in any linear system on a general K3 surface. The second problem is about the singularities of a rational curve on a K3 surface. We are trying to prove that each rational curve in ;Our basic approach to both problems is by degeneration. In summary, we degenerate general K3 surfaces to some "special" ones and by studying and the limits of rational curves on these special K3 surfaces we will be able to derive the properties of rational curves on a general K3 surface. |
