Seshadri positive submanifolds of polarized manifolds

Bădescu, Lucian; Beltrametti, Mauro C.

doi:10.2478/s11533-012-0146-z

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…However, one can compute χ(H 1,Z ) as one computes h 0 in Theorem 7.5 for the divisors H Z , H S [2] , H Y . Thus one obtains χ(H 1,Z ) = 1 2 χ(H) + 1 16 h Σ1,S×S .…”

Section: N S( S × S)mentioning

confidence: 99%

Calabi–Yau Quotients of Hyperkähler Four-folds

Camere¹,

Garbagnati²,

Mongardi³

2019

Can. J. Math.-J. Can. Math.

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The aim of this paper is to construct Calabi-Yau 4-folds as crepant resolutions of the quotients of a hyperkähler 4-fold X by a non symplectic involution α. We first compute the Hodge numbers of a Calabi-Yau constructed in this way in a general setting and then we apply the results to several specific examples of non symplectic involutions, producing Calabi-Yau 4-folds with different Hodge diamonds. Then we restrict ourselves to the case where X is the Hilbert scheme of two points on a K3 surface S and the involution α is induced by a non symplectic involution on the K3 surface. In this case we compare the Calabi-Yau 4-fold Y S , which is the crepant resolution of X/α, with the Calabi-Yau 4-fold Z S , constructed from S through the Borcea-Voisin construction. We give several explicit geometrical examples of both these Calabi-Yau 4-folds describing maps related to interesting linear systems as well as a rational 2 : 1 map from Z S to Y S .One can directly check that there are no mirror pairs in the previous table, except for the self-mirror Calabi-Yau Y S associated to the values N ′ = N + 1 for N = 1, . . . , 5.

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“…However, one can compute χ(H 1,Z ) as one computes h 0 in Theorem 7.5 for the divisors H Z , H S [2] , H Y . Thus one obtains χ(H 1,Z ) = 1 2 χ(H) + 1 16 h Σ1,S×S .…”

Section: N S( S × S)mentioning

confidence: 99%

Calabi–Yau Quotients of Hyperkähler Four-folds

Camere¹,

Garbagnati²,

Mongardi³

2019

Can. J. Math.-J. Can. Math.

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“…Many equalities and vanishings of some terms in the formulas above use the following equality for α ∈ A 4−n (X) (easy generalization of [BaBel,Lemma 1.1]):…”

Section: 2mentioning

confidence: 99%

Projective models of Nikulin orbifolds

Camere¹,

Garbagnati²,

Kapustka³

et al. 2021

Preprint

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We study projective fourfolds of K3 [2] -type with a symplectic involution and the deformations of their quotients, called orbifolds of Nikulin types; they are IHS orbifolds. We compute the Riemann-Roch formula for Weil divisors on such orbifolds and describe the first complete family of orbifolds of Nikulin type with a polarization of degree 2 as double covers of special complete intersections (3, 4) in P 6 .

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Seshadri positive submanifolds of polarized manifolds

Cited by 2 publications

References 32 publications

Calabi–Yau Quotients of Hyperkähler Four-folds

Calabi–Yau Quotients of Hyperkähler Four-folds

Projective models of Nikulin orbifolds

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