Results 1  10
of
85,467
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 ..."
Abstract

Cited by 529 (3 self)
 Add to MetaCart
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. ..."
Abstract
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 191 (10 self)
 Add to MetaCart
. 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
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 ..."
Abstract

Cited by 277 (14 self)
 Add to MetaCart
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
Perturbative derivation of mirror symmetry
"... We provide a purely perturbative (one loop) derivation of mirror symmetry for supersymmetric sigma models in two dimensions. September ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We provide a purely perturbative (one loop) derivation of mirror symmetry for supersymmetric sigma models in two dimensions. September
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 ..."
Abstract

Cited by 467 (20 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 63 (12 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
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
Mirror symmetry for abelian varieties
 J. Algebraic Geom
"... 0.1. We define the relation of mirror symmetry on the class of pairs (complex abelian variety A + an element of the complexified ample cone of A) and study its properties. More precisely, let A be a complex abelian variety, C a A ⊂ NSA(R) – the ample cone of A and put ..."
Abstract

Cited by 28 (4 self)
 Add to MetaCart
0.1. We define the relation of mirror symmetry on the class of pairs (complex abelian variety A + an element of the complexified ample cone of A) and study its properties. More precisely, let A be a complex abelian variety, C a A ⊂ NSA(R) – the ample cone of A and put
Results 1  10
of
85,467