The k�hler cone on Calabi-Yau threefolds

Wilson, P. Μ. H.

doi:10.1007/bf01231902

Cited by 122 publications

(196 citation statements)

References 26 publications

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“…Using the construction of [9], the mirror of M 1 = IP 4 (1,1,2,2,2) [8] may be identified with the family of Calabi-Yau threefolds of the form {p = 0}/G, where…”

Section: Basic Factsmentioning

confidence: 99%

Mirror symmetry for two-parameter models (I)

Candelas¹,

Ossa²,

Font³

et al. 1994

Nuclear Physics B

265

751

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We study, by means of mirror symmetry, the quantum geometry of the Kähler-class parameters of a number of Calabi-Yau manifolds that have b 11 = 2. Our main interest lies in the structure of the moduli space and in the loci corresponding to singular models. This structure is considerably richer when there are two parameters than in the various one-parameter models that have been studied hitherto. We describe the intrinsic structure of the point in the (compactification of the) moduli space that corresponds to the large complex structure or classical limit. The instanton expansions are of interest owing to the fact that some of the instantons belong to families with continuous parameters. We compute the Yukawa couplings and their expansions in terms of instantons of genus zero. By making use of recent results of Bershadsky et al. we compute also the instanton numbers for instantons of genus one. For particular values of the parameters the models become birational to certain models with one parameter. The compactification divisor of the moduli space thus contains copies of the moduli spaces of one parameter models. Our discussion proceeds via the particular models IP 4

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“…Using the construction of [9], the mirror of M 1 = IP 4 (1,1,2,2,2) [8] may be identified with the family of Calabi-Yau threefolds of the form {p = 0}/G, where…”

Section: Basic Factsmentioning

confidence: 99%

Mirror symmetry for two-parameter models (I)

Candelas¹,

Ossa²,

Font³

et al. 1994

Nuclear Physics B

265

751

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“…A zero weight must represent an uncharged hypermultiplet and therefore a modulus. We may use the work of Wilson [28] to demonstrate this. Wilson showed that a Calabi-Yau threefold containing a ruled surface M x P 1 has a moduli space which preserves this ruled surface only in codimension g{M).…”

Section: Counting Hypermultipletsmentioning

confidence: 99%

Lie groups, Calabi–Yau threefolds, and $F$-theory

Aspinwall¹,

Katz

Morrison³

2000

Advances in Theoretical and Mathematical Physics

184

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The F-theory vacuum constructed from an elliptic CalabiYau threefold with section yields an effective six-dimensional theory. The Lie algebra of the gauge sector of this theory and its representation on the space of massless hypermultiplets are e-print archive: http://xxx.lanLgov/hep-th/0002012 96 P.S. ASPINWALL, S. KATZ, AND D.R. MORRISON shown to be determined by the intersection theory of the homology of the Calabi-Yau threefold. (Similar statements hold for M-theory and the type IIA string compactified on the threefold, where there is also a dependence on the expectation values of the Ramond-Ramond fields.) We describe general rules for computing the hypermultiplet spectrum of any F-theory vacuum, including vacua with non-simply-laced gauge groups. The case of monodromy acting on a curve of Aeven singularities is shown to be particularly interesting and leads to some unexpected rules for how 2-branes are allowed to wrap certain 2-cycles. We also review the peculiar numerical predictions for the geometry of elliptic Calabi-Yau threefolds with section which arise from anomaly cancellation in six dimensions.

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“…According to [57], these walls consist of divisor classes which contractC i (i.e. the divisors intersect each curve in the locus trivially).…”

mentioning

confidence: 99%

Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

1995

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The moduli dependence of (2, 2) superstring compactifications based on CalabiYau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg orbifolds with c = 9 whose potential is a sum of A-type singularities. Here we consider the generalization to arbitrary quasi-homogeneous singularities at c = 9. We use mirror symmetry to derive the dependence of the models on the complexified Kähler moduli and check the expansions of some topological correlation functions against explicit genus zero and genus one instanton calculations. As an important application we give examples of how non-algebraic ("twisted") deformations can be mapped to algebraic ones, hence allowing us to study the full moduli space. We also study how moduli spaces can be nested in each other, thus enabling a (singular) transition from one theory to another. Following the recent work of Greene, Morrison and Strominger we show that this corresponds to black hole condensation in type II string theories compactified on Calabi-Yau manifolds. CERN-TH-7528/956/95

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The k�hler cone on Calabi-Yau threefolds

Cited by 122 publications

References 26 publications

Mirror symmetry for two-parameter models (I)

Mirror symmetry for two-parameter models (I)

Lie groups, Calabi–Yau threefolds, and $F$-theory

Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

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