Hard Lefschetz for Chow groups of generalized Kummer varieties

Laterveer, Robert

doi:10.1007/s12188-016-0140-7

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…Is it true that there are isomorphisms

\cdot L^{2 m - 2 i + j} : A_{(j)}^{i} false(X false) \overset{≅}{\to} A_{(j)}^{2 m - i + j} false(X false) for all 0 \leq 2 i - j \leq 2 m ?

(ii)Let

L \in A^{1} false(X false)

be a big line bundle. Is it true that there are isomorphisms

\cdot L^{2 m - i} : A_{(i)}^{i} false(X false) \overset{≅}{\to} A_{(i)}^{2 m} false(X false) for all 0 \leq i \leq 2 m ?

The answer to the first question is “yes” for generalized Kummer varieties . The answer to both questions is “I don't know” for Hilbert schemes of K 3 surfaces.…”

Section: Hard Lefschetzmentioning

confidence: 99%

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Algebraic cycles and EPW cubes

Laterveer

2018

Mathematische Nachrichten

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Let $X$ be a hyperk\"ahler variety with an anti-symplectic involution $\iota$. According to Beauville's conjectural "splitting property", the Chow groups of $X$ should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch-Beilinson conjectures predict how $\iota$ should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a $19$-dimensional family of hyperk\"ahler sixfolds that are "double EPW cubes" (in the sense of Iliev-Kapustka-Kapustka-Ranestad). This has interesting consequences for the Chow ring of the quotient $X/\iota$, which is an "EPW cube" (in the sense of Iliev-Kapustka-Kapustka-Ranestad).Comment: 32 pages, to appear in Math. Nachrichten, feedback welcom

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“…Is it true that there are isomorphisms

\cdot L^{2 m - 2 i + j} : A_{(j)}^{i} false(X false) \overset{≅}{\to} A_{(j)}^{2 m - i + j} false(X false) for all 0 \leq 2 i - j \leq 2 m ?

(ii)Let

L \in A^{1} false(X false)

be a big line bundle. Is it true that there are isomorphisms

\cdot L^{2 m - i} : A_{(i)}^{i} false(X false) \overset{≅}{\to} A_{(i)}^{2 m} false(X false) for all 0 \leq i \leq 2 m ?

The answer to the first question is “yes” for generalized Kummer varieties . The answer to both questions is “I don't know” for Hilbert schemes of K 3 surfaces.…”

Section: Hard Lefschetzmentioning

confidence: 99%

“…The answer to the first question is "yes" for generalized Kummer varieties [20]. The answer to both questions is "I don't know" for Hilbert schemes of K3 surfaces.…”

Section: Let Us Now Define the Modified Relative Correspondencesmentioning

confidence: 99%

Algebraic cycles and EPW cubes

Laterveer

2018

Mathematische Nachrichten

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“…The answer to the first question is "yes" for generalized Kummer varieties [27]. The answer to both questions is "I don't know, except for i = 2 and g low" for Hilbert schemes of genus g K3 surfaces.…”

Section: Corollary 34 Now Follows From What We Have Said Above In Vmentioning

confidence: 99%