Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Guo, Hanfei; Liu, Zhiyu; Zhang, Shizhuo

doi:10.48550/arxiv.2203.05442

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…This is not proven in [31]; what is known [31,Proposition 5.17] is that either the two maps agree, or the modular construction gives the double EPW sextic that is dual to the Iliev-Manivel construction. (For completeness, we should mention the recent work [20], where it is shown that ν P P Z actually agrees with ν.) Either way, the morphism ν P P Z : M • GM 4 → M dEP W is dominant.…”

Section: 2mentioning

confidence: 82%

Zero-cycles on double EPW sextics

Laterveer

Vial

2020

Commun. Contemp. Math.

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The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First, we prove a Beauville–Voisin type theorem for zero-cycles on double EPW sextics; precisely, we show that the codimension-4 part of the subring of the Chow ring of a double EPW sextic generated by divisors, the Chern classes and codimension-2 cycles invariant under the anti-symplectic covering involution has rank one. Second, for double EPW sextics birational to the Hilbert square of a K3 surface, we show that the action of the anti-symplectic involution on the Chow group of zero-cycles commutes with the Fourier decomposition of Shen–Vial.

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Section: 2mentioning

confidence: 82%

Zero-cycles on double EPW sextics

Laterveer

Vial

2020

Commun. Contemp. Math.

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“…In [26], the authors generalize Theorem 9.2 to all prime Fano threefolds of genus g ⩾ 6. In [18], the authors prove a birational categorical Torelli theorem for general non-Hodge-special Gushel-Mukai fourfolds.…”

Section: Categorical Torelli Theoremsmentioning

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.

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Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Cited by 2 publications

References 15 publications

Zero-cycles on double EPW sextics

Zero-cycles on double EPW sextics

Categorical Torelli theorems for Gushel–Mukai threefolds

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