Are minimal degree rational curves determined by their tangent vectors?

Stefan Kebekus; Sandor J. Kovacs

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arXiv · math/0206193

Are minimal degree rational curves determined by their tangent vectors?

Stefan Kebekus·Sandor J. Kovacs

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Abstract

Let X be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this setup, characterization and classification problems lead to the natural question: "Given two points on X, how many minimal degree rational curve are there which contain those points?". A recent answer to this question led to a number of new results in classification theory. As an infinitesimal analogue, we ask "How many minimal degree rational curves exist which contain a prescribed tangent vector?" In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of X is contained in at most one rational curve minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.

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BibTeX RIS

Stefan Kebekus, Sandor J. Kovacs. 2002-10-17. Are minimal degree rational curves determined by their tangent vectors?. https://arxiv.org/abs/math/0206193

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