PreprintarXiv licencearXiv
Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$
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.
Related
- Stability conditions on products of curves and Hilbert schemes of surfaces
- Degree growth for tame automorphisms of an affine quadric threefold
- Counting Rational Points on a Certain Bihomogeneous Threefold
- Non-reducedness of the Hilbert schemes of few points
- Hochschild cohomology of Hilbert schemes of points on surfaces
BibTeX
@misc{chung2026hilbert,
title = {{Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$}},
author = {Kiryong Chung and Dae-Won Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08176},
eprint = {2609.08176},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08176},
}
RIS
TY - UNPB
TI - Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$
AU - Kiryong Chung
AU - Dae-Won Lee
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08176
UR - https://arxiv.org/abs/2609.08176
AB - 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.
ER -