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Moduli spaces of rational curves on Fano threefolds (2010.06795v3)
Published 14 Oct 2020 in math.AG
Abstract: We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key to our approach is Geometric Manin's Conjecture which predicts the number of components parameterizing free curves.
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