Compactification of the moduli space of minimal instantons on the Fano 3-fold V5

Qin, Xuqiang

doi:10.1016/j.jpaa.2020.106526

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…First, we show that every Gieseker-semistable sheaf E is in the Kuznetsov component Ku(Y ). When d = 4 and 5, this is shown in [Qin19] and [Qin21b] by using the classification of instanton sheaves. We give another proof, which not need classification results on Y 1 and Y 2 , and also valid for d = 3, 4, 5.…”

Section: Moduli Of Instanton Sheaves On Y D As Bridgeland Moduli Spacementioning

confidence: 90%

“…Let Y = Y 3 , Y 4 or Y 5 . We collect some properties and classification of instanton sheaves from [Dru00], [Kuz12], [Qin19] and [Qin21b].…”

Section: Now Note That Chmentioning

confidence: 99%

“…In our note, we identify moduli space of instanton sheaves with minimal charge on Y d , d = 3, 4, 5 with moduli space of (semi)stable objects of (−4)-class 2(1 − L) in Ku(Y d ). On cubic threefolds, these Bridgeland moduli spaces were studied in [LMS15] via derived category of coherent sheaves of P 2 with the action of a sheaf of Clifford algebras, and on Y 4 , Y 5 these were studied in [Qin19] and [Qin21b] via classical stability of sheaves on curves and representations of quivers.…”

mentioning

confidence: 99%

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A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$

Liu¹,

Zhang²

2021

Preprint

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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 C(X) of conics, moduli spaces of semistable sheaves M X (2, 1, 6) and M X (2, −1, 6) and the correspondent moduli spaces on cubic threefold Y 3 are realized by moduli spaces of stable vector bundles M b Y (2, 1, 2) and M b Y (2, −1, 2). We show that moduli spaces of semistable objects of (−4)-classes on Y d are isomorphic to the moduli spaces of instanton sheaves M inst Y when d = 1, 2, and show that there're open immersions of M inst Y into moduli spaces of semistable objects of (−4)-classes when d = 1, 2. Finally, when d = 4, 5 we show that these moduli spaces are all isomorphic to M ss X (2, 0, 4).

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Section: Moduli Of Instanton Sheaves On Y D As Bridgeland Moduli Spacementioning

confidence: 90%

“…Let Y = Y 3 , Y 4 or Y 5 . We collect some properties and classification of instanton sheaves from [Dru00], [Kuz12], [Qin19] and [Qin21b].…”

Section: Now Note That Chmentioning

confidence: 99%

mentioning

confidence: 99%

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A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$

Liu¹,

Zhang²

2021

Preprint

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“…In our note, we identify moduli space of instanton sheaves with minimal charge on Y d , d = 3, 4, 5 with moduli space of (semi)stable objects of (−4)-class 2v in Ku(Y d ). On cubic threefolds, these Bridgeland moduli spaces were studied in [29] via derived category of coherent sheaves of P 2 with the action of a sheaf of Clifford algebras, and on Y 4 , Y 5 these were studied in [37,39] via classical stability of sheaves on curves and representations of quivers.…”

Section: Related Workmentioning

confidence: 99%

“…We collect some properties and classifications of instanton sheaves from [17,27,37,39]. Recall that on a smooth conic C ∼ = P 1 , the theta-characteristic is given by θ ∼ = O P 1 (−1).…”

Section: When D = 1 We Have (1) Implies (2)mentioning

confidence: 99%

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $$X_{14}$$ and $$Y_3$$

Liu

Zhang

2022

Math. Z.

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We study Bridgeland moduli spaces of semistable objects of $$(-1)$$ ( - 1 ) -classes and $$(-4)$$ ( - 4 ) -classes in the Kuznetsov components on index one prime Fano threefold $$X_{4d+2}$$ X 4 d + 2 of degree $$4d+2$$ 4 d + 2 and index two prime Fano threefold $$Y_d$$ Y d of degree d for $$d=3,4,5$$ d = 3 , 4 , 5 . For every Serre-invariant stability condition on the Kuznetsov components, we show that the moduli spaces of stable objects of $$(-1)$$ ( - 1 ) -classes on $$X_{4d+2}$$ X 4 d + 2 and $$Y_d$$ Y d are isomorphic. We show that moduli spaces of stable objects of $$(-1)$$ ( - 1 ) -classes on $$X_{14}$$ X 14 are realized by Fano surface $$\mathcal {C}(X)$$ C ( X ) of conics, moduli spaces of semistable sheaves $$M_X(2,1,6)$$ M X ( 2 , 1 , 6 ) and $$M_X(2,-1,6)$$ M X ( 2 , - 1 , 6 ) and the correspondent moduli spaces on cubic threefold $$Y_3$$ Y 3 are realized by moduli spaces of stable vector bundles $$M^b_Y(2,1,2)$$ M Y b ( 2 , 1 , 2 ) and $$M^b_Y(2,-1,2)$$ M Y b ( 2 , - 1 , 2 ) . We show that moduli spaces of semistable objects of $$(-4)$$ ( - 4 ) -classes on $$Y_{d}$$ Y d are isomorphic to the moduli spaces of instanton sheaves $$M^{inst}_Y$$ M Y inst when $$d\ne 1,2$$ d ≠ 1 , 2 , and show that there are open immersions of $$M^{inst}_Y$$ M Y inst into moduli spaces of semistable objects of $$(-4)$$ ( - 4 ) -classes when $$d=1,2$$ d = 1 , 2 . Finally, when $$d=3,4,5$$ d = 3 , 4 , 5 we show that these moduli spaces are all isomorphic to $$M^{ss}_X(2,0,4)$$ M X ss ( 2 , 0 , 4 ) .

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Instanton sheaves on Fano threefolds

Comaschi,

Jardim

2024

manuscripta math.

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Compactification of the moduli space of minimal instantons on the Fano 3-fold V5

Cited by 8 publications

References 16 publications

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$

A note on Bridgeland moduli spaces and moduli spaces of sheaves on $$X_{14}$$ and $$Y_3$$

Instanton sheaves on Fano threefolds

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