Simple models of quasihomogeneous projective 3-folds.
Positive sheaves of differentials coming from coarse moduli spaces
Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base , and suppose the family is non-isotrivial. If is a smooth compactification of , such that is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along . Viehweg and Zuo have shown that for some , the symmetric power of this sheaf admits many sections. More precisely, the symmetric power contains an invertible...
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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