Abstract
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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