2015
DOI: 10.1007/s00209-015-1434-7
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Periods of double EPW-sextics

Abstract: We study the period map for double EPW-sextics, which are varieties making up a locally versal family of polarized hyperkaehler fourfolds. Double EPW-sextics are parametrized by Lagrangian subspaces of the third wedge-product of a 6-dimensional complex vector space. We prove that Lagrangians in the indeterminacy locus of the period map contain\ud a decomposable 3-vector enjoying very special properties. In addition we prove a result about periods of double EPW-sextics which are either smooth or have isolated s… Show more

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Cited by 20 publications
(26 citation statements)
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“…Since our constructions are inductive, and since the geometric behavior (for hyperelliptic quartics) identified in [LO18a] matches what we predicted in [LO18b] (for quartics), we have no doubt of the validity of our conjecture for quartic surfaces. Similarly, earlier work on EPW sextics [O’Gr15, O’Gr16] seems compatible with our conjectures; presumably our predictions (for ) can be checked inductively.…”
Section: Introductionsupporting
confidence: 90%
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“…Since our constructions are inductive, and since the geometric behavior (for hyperelliptic quartics) identified in [LO18a] matches what we predicted in [LO18b] (for quartics), we have no doubt of the validity of our conjecture for quartic surfaces. Similarly, earlier work on EPW sextics [O’Gr15, O’Gr16] seems compatible with our conjectures; presumably our predictions (for ) can be checked inductively.…”
Section: Introductionsupporting
confidence: 90%
“…As is well known, the period space for quartic surfaces is , and the latter is equal to by Proposition 1.2.3. We will prove that is the period space of hyperelliptic quartic surfaces, see § 2.2, and that is the period space of desingularized EPW sextics (a quotient of the period space of double EPW sextics by the natural duality involution; see [O’Gr15]). Lastly, in § 2.3, we will establish a relation between and the period space of hyperkähler -folds of Type OG10.…”
Section: Locally Symmetric Spaces As Period Spaces Formentioning
confidence: 99%
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“…In Section 3, we discuss a relation between complex GM varieties and Eisenbud-Popescu-Walter (EPW) sextics [EPW01,OGr06]. An EPW sextic is a hypersurface of degree 6 in the projectivization P(V 6 ) of a 6-dimensional vector space V 6 which depends on the choice of a Lagrangian subspace A ⊂ 3 V 6 .…”
Section: Introductionmentioning
confidence: 99%
“…We say has no decomposable vectors if does not intersect . O’Grady [O’Gr06, O’Gr08, O’Gr16, O’Gr12, O’Gr13, O’Gr15] extensively investigated the geometry of EPW sextics, and proved in particular that (see also [DK18a, Theorem B.2]) if has no decomposable vectors, then:…”
Section: Conjectures On Duality and Rationalitymentioning
confidence: 99%