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arXiv · 1702.08508

Geometric Manin's Conjecture and rational curves

Brian Lehmann·Sho Tanimoto
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Abstract

Let $X$ be a smooth projective Fano variety over the complex numbers. We study the moduli spaces 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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Brian Lehmann, Sho Tanimoto. 2017-02-27. Geometric Manin's Conjecture and rational curves. https://doi.org/10.1112/s0010437x19007103

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