Singular rational curves on elliptic K3 surfaces |
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Authors: | Jonas Baltes |
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Affiliation: | Mathematisches Institut, Georg-August-Universität Göttingen, Niedersachsen, Germany |
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Abstract: | We show that on every elliptic K3 surface there are rational curves such that , that is, of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to is dense in the Zariski topology. As an application, we give a simple proof of a theorem of Kobayashi in the elliptic case, that is, there are no globally defined symmetric differential forms. |
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Keywords: | elliptic K3 surfaces K3 surfaces rational curves |
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