A note on the Kuznetsov component of the Veronese double cone

Petkovic, Marin; Rota, Franco

doi:10.1016/j.jpaa.2022.107214

Cited by 4 publications

(1 citation statement)

References 19 publications

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“…When

F

is not

\sigma ^0_{\alpha, \beta }

‐semistable for

(\alpha, \beta)\in V

, the argument is more complicated. Our main tools are the inequalities in [49, 51, Proposition 4.1], Lemma 4.6, and Theorem 4.7, which allow us to bound the rank and first two Chern characters

\mathrm{ch}_1,\mathrm{ch}_2

of the destabilizing objects and their cohomology objects. Since

F\in \mathcal {A}_X

, by using the Euler characteristics

\chi (\mathcal {O}_X,-)

and

\chi (\mathcal {E}^{\vee },-)

, we can obtain a bound on

\mathrm{ch}_3

.…”

Section: Conics and Bridgeland Moduli Spacesmentioning

confidence: 99%

Categorical Torelli theorems for Gushel–Mukai threefolds

Jacovskis,

Lin,

Liu

et al. 2024

Journal of London Math Soc

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We show that a general ordinary Gushel–Mukai (GM) threefold can be reconstructed from its Kuznetsov component together with an extra piece of data coming from tautological subbundle of the Grassmannian . We also prove that determines the birational isomorphism class of , while determines the isomorphism class of a special GM threefold if it is general. As an application, we prove a conjecture of Kuznetsov–Perry in dimension 3 under a mild assumption. Finally, we use to restate a conjecture of Debarre–Iliev–Manivel regarding fibers of the period map for ordinary GM threefolds.

show abstract

“…When

F

is not

\sigma ^0_{\alpha, \beta }

‐semistable for

(\alpha, \beta)\in V

, the argument is more complicated. Our main tools are the inequalities in [49, 51, Proposition 4.1], Lemma 4.6, and Theorem 4.7, which allow us to bound the rank and first two Chern characters

\mathrm{ch}_1,\mathrm{ch}_2

of the destabilizing objects and their cohomology objects. Since

F\in \mathcal {A}_X

, by using the Euler characteristics

\chi (\mathcal {O}_X,-)

and

\chi (\mathcal {E}^{\vee },-)

, we can obtain a bound on

\mathrm{ch}_3

.…”

Section: Conics and Bridgeland Moduli Spacesmentioning

confidence: 99%

Categorical Torelli theorems for Gushel–Mukai threefolds

Jacovskis,

Lin,

Liu

et al. 2024

Journal of London Math Soc

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Some Remarks on Fano Three-Folds of Index Two and Stability Conditions

Pertusi

Song

2021

International Mathematics Research Notices

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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 ${\operatorname{\mathsf{Ku}}}(X)$, 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 ${\operatorname{\mathsf{Ku}}}(X)$ preserves these stability conditions. As an application, we obtain the smoothness of nonempty moduli spaces of stable objects in ${\operatorname{\mathsf{Ku}}}(X)$. When $X$ is a quartic double solid, we describe a connected component of the stability manifold parametrizing stability conditions on ${\operatorname{\mathsf{Ku}}}(X)$.

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Bridgeland stability of minimal instanton bundles on Fano threefolds

Qin

2023

J. Math. Soc. Japan

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A note on the Kuznetsov component of the Veronese double cone

Cited by 4 publications

References 19 publications

Categorical Torelli theorems for Gushel–Mukai threefolds

Categorical Torelli theorems for Gushel–Mukai threefolds

Some Remarks on Fano Three-Folds of Index Two and Stability Conditions

Bridgeland stability of minimal instanton bundles on Fano threefolds

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