We prove that ideal sheaves of lines in a Fano three-fold X of Picard rank one and index two are stable objects in the Kuznetsov component Ku(X)⁠, with respect to the stability conditions constructed by Bayer, Lahoz, Macrì, and Stellari, giving a modular description to the Hilbert scheme of lines in X⁠. When X is a cubic three-fold, we show that the Serre functor of Ku(X) preserves these stability conditions. As an application, we obtain the smoothness of nonempty moduli spaces of stable objects in Ku(X)⁠. When X is a quartic double solid, we describe a connected component of the stability manifold parametrizing stability conditions on Ku(X)⁠.

Some remarks on Fano threefolds of index two and stability conditions / S. Yang, L. Pertusi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - (2021 May 10). [Epub ahead of print] [10.1093/imrn/rnaa387]

Some remarks on Fano threefolds of index two and stability conditions

L. Pertusi
2021

Abstract

We prove that ideal sheaves of lines in a Fano three-fold X of Picard rank one and index two are stable objects in the Kuznetsov component Ku(X)⁠, with respect to the stability conditions constructed by Bayer, Lahoz, Macrì, and Stellari, giving a modular description to the Hilbert scheme of lines in X⁠. When X is a cubic three-fold, we show that the Serre functor of Ku(X) preserves these stability conditions. As an application, we obtain the smoothness of nonempty moduli spaces of stable objects in Ku(X)⁠. When X is a quartic double solid, we describe a connected component of the stability manifold parametrizing stability conditions on Ku(X)⁠.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/870883
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