A note on the Kuznetsov component of the Veronese double cone
Abstract
This note describes moduli spaces of complexes in the derived category of a Veronese double cone . Focusing on objects with the same class as ideal sheaves of lines, we describe the moduli space of Gieseker stable sheaves and show that it has two components. Then, we study the moduli space of stable complexes in the Kuznetsov component of of the same class, which also has two components. One parametrizes ideal sheaves of lines and it appears in both moduli spaces. The other components are not directly related by a wall-crossing: we show this by describing an intermediate moduli space of complexes as a space of stable pairs in the sense of Pandharipande and Thomas.
Keywords
Cite
@article{arxiv.2007.05555,
title = {A note on the Kuznetsov component of the Veronese double cone},
author = {Marin Petkovic and Franco Rota},
journal= {arXiv preprint arXiv:2007.05555},
year = {2023}
}
Comments
V2: 19 pages. Substantially rewritten. Added results on Hilbert scheme of lines, improved exposition, strengthened arguments. References and acknowledgments updated. V3: Final version, to appear in J. Pure Appl. Algebra. The statement of theorem 5.1 contained an imprecision, now corrected. All comments very welcome!