Geometric Manin's Conjecture and rational curves
Algebraic Geometry
2019-04-17 v3
Abstract
Let be a smooth projective Fano variety over the complex numbers. We study the moduli spaces of rational curves on using the perspective of Manin's Conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on . We propose a Geometric Manin's Conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.
Cite
@article{arxiv.1702.08508,
title = {Geometric Manin's Conjecture and rational curves},
author = {Brian Lehmann and Sho Tanimoto},
journal= {arXiv preprint arXiv:1702.08508},
year = {2019}
}
Comments
29 pages; a minor gap in Section 7 has been addressed. To appear in Compositio Mathematica