On the minimal number of singular fibres in a family of surfaces of general type.
The cone of curves of a K3 surface.
Holomorphic one-forms on varieties of general type
Are rational curves determined by tangent vectors?
Let be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of is contained in at most one rational curve of minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.
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