Year: 2026
Type: preprint
Abstract: We present a new construction that allows us to break off large-degree rational curves from families of higher genus curves. Our construction and results deepen the connection between rational curves and positivity of the anticanonical divisor. Specifically, we show that varieties with large Fujita invariant admit large families of rational curves. We also construct free rational curves on certain singular Fano varieties. As an explicit consequence of our results, we prove that for a general Fano hypersurface of index at least 3, all spaces of genus g curves of sufficiently large degree have the expected dimension.
Source: arXiv (Cornell University)
Authors: Jovinelly, Eric, Lehmann, Brian, Riedl, Eric
Institutions: Boston College, University of Notre Dame
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204769823