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Geometric Manin’s conjecture and rational curves

  • Brian Lehmann (a1) and Sho Tanimoto (a2) (a3)


Let $X$ be a smooth projective Fano variety over the complex numbers. We study the moduli space of rational curves on $X$ using the perspective of Manin’s conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on $X$ . We propose a geometric Manin’s conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.



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Lehmann is supported by NSF grant 1600875. Tanimoto is partially supported by Lars Hesselholt’s Niels Bohr professorship, and MEXT Japan, Leading Initiative for Excellent Young Researchers (LEADER).



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Geometric Manin’s conjecture and rational curves

  • Brian Lehmann (a1) and Sho Tanimoto (a2) (a3)


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