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Generalized CalabiYau manifolds
 Q. J. Math
"... A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case o ..."
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Cited by 330 (3 self)
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A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case
Superconformal field theory on threebranes at a CalabiYau singularity
 Nucl. Phys. B
, 1998
"... Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue that ..."
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Cited by 690 (37 self)
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Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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by a Newton polyhedron ∆ consists of (n − 1)dimensional CalabiYau varieties then the dual, or polar, polyhedron ∆ ∗ in the dual space defines another family F( ∆ ∗ ) of CalabiYau varieties, so that we obtain the remarkable duality between two different families of CalabiYau varieties. It is shown
CFT’s from CalabiYau Fourfolds
 Nucl. Phys. B584
"... We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a CalabiYau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated ..."
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Cited by 277 (14 self)
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We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a CalabiYau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated
Acyclic CalabiYau categories
"... We prove a structure theorem for triangulated CalabiYau categories: An algebraic 2CalabiYau triangulated category over an algebraically closed field is a cluster category iff it contains a cluster tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization for hi ..."
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Cited by 37 (8 self)
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We prove a structure theorem for triangulated CalabiYau categories: An algebraic 2CalabiYau triangulated category over an algebraically closed field is a cluster category iff it contains a cluster tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization
Singular CalabiYau Manifolds
, 2000
"... We study superstring propagations on the CalabiYau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N = 2 LandauGinzburg theory and Liouville theory. If the LandauGinzburg description precisely reflects the in ..."
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the information of ADE singularity, the LandauGinzburg model of D4,E6,E8 and Gepner model of A2 ⊗ A2,A2 ⊗ A3,A2 ⊗ A4 should give the same result. We compute the elements of D4,E6,E8 modular invariants for the singular CalabiYau compactification in terms of the spectral flow invariant orbits of the tensor
Convergence of CalabiYau manifolds
, 2009
"... In this paper, we study the convergence of CalabiYau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of CalabiYau manifolds. ..."
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Cited by 14 (3 self)
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In this paper, we study the convergence of CalabiYau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of CalabiYau manifolds.
RR flux on CalabiYau and partial supersymmetry breaking
 Phys. Lett. B
, 2000
"... We show how turning on Flux for RR (and NSNS) field strengths on noncompact CalabiYau 3folds can serve as a way to partially break supersymmetry from N = 2 to N = 1 by mass deformation. The freezing of the moduli of CalabiYau in the presence of the flux is the familiar phenomenon of freezing of ..."
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Cited by 201 (9 self)
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We show how turning on Flux for RR (and NSNS) field strengths on noncompact CalabiYau 3folds can serve as a way to partially break supersymmetry from N = 2 to N = 1 by mass deformation. The freezing of the moduli of CalabiYau in the presence of the flux is the familiar phenomenon of freezing
Tables of Calabi–Yau equations
, 2005
"... The main part of this paper is a big table (see Appendix A) containing what we believe to be a complete list of all fourth order equations of Calabi–Yau type known so far. In the text preceding the tables we explain what a differential equation of Calabi–Yau type is and we briefly discuss how we fou ..."
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Cited by 12 (0 self)
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The main part of this paper is a big table (see Appendix A) containing what we believe to be a complete list of all fourth order equations of Calabi–Yau type known so far. In the text preceding the tables we explain what a differential equation of Calabi–Yau type is and we briefly discuss how we
ARITHMETIC OF CALABI–YAU VARIETIES
, 2004
"... ... of Göttingen. We address the modularity questions of Calabi–Yau varieties of dimension ≤ 3 defined over Q. The uptodate reference on the modularity of Calabi–Yau varieties is Yui [Yu03]. ..."
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Cited by 2 (0 self)
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... of Göttingen. We address the modularity questions of Calabi–Yau varieties of dimension ≤ 3 defined over Q. The uptodate reference on the modularity of Calabi–Yau varieties is Yui [Yu03].
Results 1  10
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