English

Moduli spaces of rational curves on Fano threefolds

Algebraic Geometry 2022-07-12 v3

Abstract

We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key to our approach is Geometric Manin's Conjecture which predicts the number of components parameterizing free curves.

Keywords

Cite

@article{arxiv.2010.06795,
  title  = {Moduli spaces of rational curves on Fano threefolds},
  author = {Roya Beheshti and Brian Lehmann and Eric Riedl and Sho Tanimoto},
  journal= {arXiv preprint arXiv:2010.06795},
  year   = {2022}
}

Comments

No change from the previous version, 51 pages, to appear in Advances in Mathematics