Classification of free actions on complete intersections of four quadrics

Hua, Zheng

doi:10.4310/atmp.2011.v15.n4.a2

Cited by 13 publications

(33 citation statements)

References 7 publications

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“…These cannot both vanish so it must be the case that Now F 0 has bidegree (3,3) in ξ and η and it is natural to ask how X 19,19 is related to the bicubic X 2,83 = P 2 P 2 The Kreuzer-Skarke list, CICY's, toric CICY's, and toric conifolds [3,[6][7][8][9], with their mirrors. The Gross-Popescu, Rødland, Tonoli, Borisov-Hua and Hua manifolds [10][11][12][13][14]. Previously known quotients by freely acting groups and their mirrors.…”

Section: Splitting and Contractionmentioning

confidence: 99%

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New Calabi‐Yau manifolds with small Hodge numbers

Candelas¹,

Davies

2010

Fortschritte der Physik

192

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It is known that many Calabi-Yau manifolds form a connected web. The question of whether all Calabi-Yau manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of Calabi-Yau manifolds where the Hodge numbers (h 11 , h 21 ) are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with χ = −6, that is an analogue of the χ = −6 manifold found by Yau, and manifolds with an attractive structure that may prove of interest for string phenomenology. We also examine the relation of some of these manifolds to the remarkable Gross-Popescu manifolds that have Euler number zero.

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Section: Splitting and Contractionmentioning

confidence: 99%

“…(-10,7) (1,6) P 4 P 4 1 1 1 1 1 [13,14,32] (-8,6) (1,5) 2.1.1 X 2,52 ; a first split of the quintic threefold…”

Section: Webs Of Transgressionsmentioning

confidence: 99%

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New Calabi‐Yau manifolds with small Hodge numbers

Candelas¹,

Davies

2010

Fortschritte der Physik

192

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“…There is a free Z 2 ×Z 2 ×Z 2 -action on X [21,23,24,28,57]. We will always divide out this group action and define…”

Section: Simple Case -A One-parameter Modelmentioning

confidence: 99%

Stabilizing all Kähler moduli in type IIB orientifolds

Bobkov

Braun

Kumar

et al. 2010

J. High Energ. Phys.

112

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We describe a simple and robust mechanism that stabilizes all Kähler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G 2 compactifications of M theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kähler moduli are worked out. We find that the stabilized volumes of all two-and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.

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“…The polynomial deformation method also yields consistent results. For this manifold the classification of free group actions was first performed by Hua et al[27].4.2 The sequence of splits:X 1,65 → X 2,58 → X 3,51 → X 4,44 → X 5,37…”

mentioning

confidence: 99%

Hodge numbers for CICYs with symmetries of order divisible by 4

2016

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We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either Z 2 or contain Z 4 , Z 2 × Z 2 , Z 3 or Z 5 as a subgroup. The Hodge numbers for the quotients for which the group G contains Z 3 or Z 5 have been computed previously. This paper deals with the remaining cases, for which G ⊇ Z 4 or G ⊇ Z 2 × Z 2 . We also compute the Hodge numbers for 99 of the 166 CICY's which have Z 2 quotients.

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Classification of free actions on complete intersections of four quadrics

Cited by 13 publications

References 7 publications

New Calabi‐Yau manifolds with small Hodge numbers

New Calabi‐Yau manifolds with small Hodge numbers

Stabilizing all Kähler moduli in type IIB orientifolds

Hodge numbers for CICYs with symmetries of order divisible by 4

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