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Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Mirror symmetry . . .
 TO APPEAR IN ESSAYS ON MIRROR MANIFOLDS II
, 1994
"... We review various constructions of mirror symmetry in terms of LandauGinzburg orbifolds for arbitrary central charge c and CalabiYau hypersurfaces and complete intersections in toric varieties. In particular it is shown how the different techniques are related. ..."
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We review various constructions of mirror symmetry in terms of LandauGinzburg orbifolds for arbitrary central charge c and CalabiYau hypersurfaces and complete intersections in toric varieties. In particular it is shown how the different techniques are related.
Orientifolds and Mirror symmetry
, 2003
"... We study parity symmetries and crosscap states in classes of N = 2 supersymmetric quantum field theories in 1+1 dimensions, including nonlinear sigma models, gauged WZW models, LandauGinzburg models, and linear sigma models. The parity anomaly and its cancellation play important roles in many of t ..."
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Cited by 271 (11 self)
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We study parity symmetries and crosscap states in classes of N = 2 supersymmetric quantum field theories in 1+1 dimensions, including nonlinear sigma models, gauged WZW models, LandauGinzburg models, and linear sigma models. The parity anomaly and its cancellation play important roles in many
Mirror Symmetry is TDuality
, 1996
"... It is argued that every CalabiYau manifold X with a mirror Y admits a family of supersymmetric toroidal 3cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to Tduality on the 3cycles. The geomet ..."
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Cited by 182 (10 self)
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. The geometry of moduli space is addressed in a general framework. Several examples are discussed. y email: andy@denali.physics.ucsb.edu yy email: yau@abel.math.harvard.edu yyy email: zaslow@abel.math.harvard.edu 1. Introduction The discovery of mirror symmetry in string theory [1] has led to a number
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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that the properties of this duality coincide with the properties of Mirror Symmetry discovered by physicists for CalabiYau 3folds. Our method allows to construct many new examples of CalabiYau 3folds and new candidates for their mirrors which were previously unknown for physicists. We conjecture that there exists
Perturbative derivation of mirror symmetry
"... We provide a purely perturbative (one loop) derivation of mirror symmetry for supersymmetric sigma models in two dimensions. September ..."
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Cited by 6 (2 self)
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We provide a purely perturbative (one loop) derivation of mirror symmetry for supersymmetric sigma models in two dimensions. September
Stringy Mirror Symmetry
"... Abstract We prove that the mirror pairs constructed by Batyrev and Borisov have stringy mirror symmetry. ..."
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Abstract We prove that the mirror pairs constructed by Batyrev and Borisov have stringy mirror symmetry.
Opening Mirror Symmetry on the Quintic
, 2006
"... Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open GromovWitten invariants, satisfies a certain extension of th ..."
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Cited by 60 (13 self)
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Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open GromovWitten invariants, satisfies a certain extension
Geometric Aspects of Mirror Symmetry
"... Abstract. The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X, Y) of Calabi–Yau threefolds, the bestunderstood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go beyo ..."
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Cited by 28 (1 self)
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Abstract. The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X, Y) of Calabi–Yau threefolds, the bestunderstood mirror statements relate certain small corners of the moduli spaces of X and of Y. We will indicate how one might go
Results 1  10
of
1,478