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PLANAR HOMOLOGICAL MIRROR SYMMETRY
, 707
"... Abstract. In this article, we formulate a planar limited version of the Bside in homological mirror symmetry that formularizes ChernSimonstype topological open string field theory using homotopy associative algebra (A ∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We sh ..."
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Abstract. In this article, we formulate a planar limited version of the Bside in homological mirror symmetry that formularizes ChernSimonstype topological open string field theory using homotopy associative algebra (A ∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We
Homological mirror symmetry in dimension one
 In Advances in
, 2001
"... Abstract. In this paper we complete the proof began by A. Polishchuk and E. Zaslow [PZ] of a weak version of Kontsevich’s homological mirror symmetry conjecture for elliptic curves. 1. ..."
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Cited by 1 (0 self)
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Abstract. In this paper we complete the proof began by A. Polishchuk and E. Zaslow [PZ] of a weak version of Kontsevich’s homological mirror symmetry conjecture for elliptic curves. 1.
Generalized Homological Mirror Symmetry and Cubics
, 2008
"... To the cherished memory of our unforgettable teacher V.A. Iskovskikh Abstract—We discuss an approach to studying Fano manifolds based on Homological Mirror Symmetry. We consider some classical examples from a new point of view. DOI: 10.1134/S0081543809010118 1. ..."
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To the cherished memory of our unforgettable teacher V.A. Iskovskikh Abstract—We discuss an approach to studying Fano manifolds based on Homological Mirror Symmetry. We consider some classical examples from a new point of view. DOI: 10.1134/S0081543809010118 1.
Homological mirror symmetry for the fourtorus
, 2009
"... Abstract. We use the quilt formalism of MauWehrheimWoodward to give a sufficient condition for a finite collection of Lagrangian submanifolds to splitgenerate the Fukaya category, and deduce homological mirror symmetry for the standard 4torus. As an application, we study Lagrangian genus two sur ..."
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Cited by 10 (3 self)
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Abstract. We use the quilt formalism of MauWehrheimWoodward to give a sufficient condition for a finite collection of Lagrangian submanifolds to splitgenerate the Fukaya category, and deduce homological mirror symmetry for the standard 4torus. As an application, we study Lagrangian genus two
HOMOLOGICAL MIRROR SYMMETRY FOR PUNCTURED SPHERES
"... Abstract. We prove that the wrapped Fukaya category of a punctured sphere (S2 with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror LandauGinzburg model, proving one side of the homological mirror symmetry conjecture in this case. By in ..."
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Cited by 17 (3 self)
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Abstract. We prove that the wrapped Fukaya category of a punctured sphere (S2 with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror LandauGinzburg model, proving one side of the homological mirror symmetry conjecture in this case
Homological mirror symmetry with higher products
 in Proceedings of the Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds, 247–259. AMS and International
, 2001
"... The homological mirror symmetry conjecture formulated by M. Kontsevich in [6] claims that derived categories of Fukaya’s symplectic A∞categogy F(M) of a CalabiYau manifold M and of coherent sheaves on a mirror dual CalabiYau manifold X are equivalent. In particular, this means that one can identif ..."
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Cited by 41 (6 self)
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The homological mirror symmetry conjecture formulated by M. Kontsevich in [6] claims that derived categories of Fukaya’s symplectic A∞categogy F(M) of a CalabiYau manifold M and of coherent sheaves on a mirror dual CalabiYau manifold X are equivalent. In particular, this means that one can
HOMOLOGICAL MIRROR SYMMETRY FOR FANO SURFACES
"... The phenomenon of mirror symmetry was first evidenced in the early 1990s as a remarkable correspondence between pairs of CalabiYau manifolds arising from a duality in string theory. Given a mirror pair (X, Y), the complex geometry of X is essentially equivalent to the symplectic geometry of Y, and ..."
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, and viceversa. The homological mirror symmetry conjecture, due to Kontsevich, treats mirror symmetry as an equivalence between two categories naturally attached to the mirror manifolds. Namely, Dbranes (boundary conditions for open strings) are expected to be coherent sheaves in one of the two models
Homological mirror symmetry for the genus two curve
"... The Homological Mirror Symmetry conjecture relates symplectic and algebraic geometry through their associated categorical structures. Kontsevich’s original version [31] concerned ..."
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Cited by 48 (2 self)
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The Homological Mirror Symmetry conjecture relates symplectic and algebraic geometry through their associated categorical structures. Kontsevich’s original version [31] concerned
Matrix Factorizations and Homological Mirror Symmetry on the Torus
, 2007
"... We consider matrix factorizations and homological mirror symmetry on the torus T 2 using a Landau–Ginzburg description. We identify the basic matrix factorizations of the Landau– Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary m ..."
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Cited by 2 (0 self)
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We consider matrix factorizations and homological mirror symmetry on the torus T 2 using a Landau–Ginzburg description. We identify the basic matrix factorizations of the Landau– Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary
Results 1  10
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123,679