2021
DOI: 10.48550/arxiv.2106.01961
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A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$

Abstract: We study Bridgeland moduli spaces of semistable objects of (−1)-classes and (−4)-classes in the Kuznetsov components on index one prime Fano threefold X 4d+2 of degree 4d + 2 and index two prime Fano threefold Y d of degree d for d = 3, 4, 5. For every Serre-invariant stability condition on the Kuznetsov components, we show that the moduli spaces of stable objects of (−1)-classes on X 4d+2 and Y d are isomorphic. We show that moduli spaces of stable objects of (−1)-classes on X 14 are realized by Fano surface … Show more

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Cited by 3 publications
(5 citation statements)
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“…In fact, the property of Serre-invariance is very helpful in the study of the properties of moduli spaces and the stability of objects, see, for instance, [18,32] for many recent applications. In [14] the notion of Serre-invariance is applied to show that the moduli space of stable Ulrich bundles of rank 𝑑 ≥ 2 on a cubic threefold is irreducible.…”
Section: Introductionmentioning
confidence: 99%
“…In fact, the property of Serre-invariance is very helpful in the study of the properties of moduli spaces and the stability of objects, see, for instance, [18,32] for many recent applications. In [14] the notion of Serre-invariance is applied to show that the moduli space of stable Ulrich bundles of rank 𝑑 ≥ 2 on a cubic threefold is irreducible.…”
Section: Introductionmentioning
confidence: 99%
“…In fact, the property of Serre-invariance is very helpful in the study of the properties of moduli spaces and the stability of objects, see for instance [JLLZ21,LZ21] for many recent applications. In [FP21] the notion of Serre-invariance is applied to show that the moduli space of stable Ulrich bundles of rank d ě 2 on a cubic threefold is irreducible.…”
Section: Introductionmentioning
confidence: 99%
“…Related works and motivations. The interest in the study of Serre-invariant stability conditions on semiorthogonal components in the bounded derived category has grown recently, mostly due to the applications to the study of moduli spaces (see for instance [PY20], [LZ21]) and to understand more the Kuznetsov component. For Fano threefolds of Picard rank 1 and index 2 the existence of Serre-invariant stability conditions on their Kuznetsov component is proved in [PY20], making use of the stability conditions constructed in [BLMS17].…”
Section: Introductionmentioning
confidence: 99%
“…Another open question is to generalise Theorem 1.3 and Corollary 6.5 to further study of moduli spaces of semistable objects in Ku(X) with respect to a Serre-invariant stability condition like their projectivity or irreducibility. Some cases of small dimension have been studied in [PY20], [APR19], [BBF + 20], [Qin21], [LZ21].…”
Section: Introductionmentioning
confidence: 99%
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