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1 results

Geometric Manin’s conjecture and rational curves
Part of
- Curves
Brian Lehmann, Sho Tanimoto
Journal:

Compositio Mathematica / Volume 155 / Issue 5 / May 2019

Published online by Cambridge University Press:

10 April 2019, pp. 833-862

Print publication:

May 2019
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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.