Year: 2026
Type: preprint
Abstract: In this paper, we give a complete description of the Hilbert schemes of rational curves up to degree $6$ on a prime Fano threefold $X$ of degree $22$. One of the key ingredients in the geometry of these Hilbert schemes is the geometry of bisecant conics associated with rational curves on $X$. As applications, we describe additional geometric features of these moduli spaces and derive Donaldson--Thomas (DT) type invariants.
Source: arXiv (Cornell University)
Authors: Chung, Kiryong, Lee, Dae-Won
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212064161