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91
Derived categories of coherent sheaves and triangulated categories of singularities
, 2005
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Lagrangian Floer theory on compact toric manifolds: Survey
, 2010
"... This is a survey of a series of papers [FOOO3, FOOO4, FOOO5]. We discuss the calculation of the Floer cohomology of Lagrangian submanifold which is a T n orbit in a compact toric manifold. Applications to symplectic topology and to mirror symmetry are also discussed. ..."
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Cited by 77 (8 self)
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This is a survey of a series of papers [FOOO3, FOOO4, FOOO5]. We discuss the calculation of the Floer cohomology of Lagrangian submanifold which is a T n orbit in a compact toric manifold. Applications to symplectic topology and to mirror symmetry are also discussed.
Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
, 2005
"... We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau ..."
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Cited by 57 (10 self)
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We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau
Mirror symmetry and Tduality in the complement of an anticanonical divisor
 J. GÖKOVA GEOM. TOPOL
"... We study the geometry of complexified moduli spaces of special Lagrangian submanifolds in the complement of an anticanonical divisor in a compact Kähler manifold. In particular, we explore the connections between Tduality and mirror symmetry in concrete examples, and show how quantum corrections ar ..."
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Cited by 55 (4 self)
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We study the geometry of complexified moduli spaces of special Lagrangian submanifolds in the complement of an anticanonical divisor in a compact Kähler manifold. In particular, we explore the connections between Tduality and mirror symmetry in concrete examples, and show how quantum corrections arise in this context.
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
Morse homology, tropical geometry, and homological mirror symmetry for toric varieties
 preprint (math.SG/0610004). SYMMETRY AND TDUALITY 41
"... Abstract. Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the LandauGinzburg ..."
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Cited by 33 (1 self)
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Abstract. Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the LandauGinzburg
Special Lagrangian fibrations, wallcrossing and mirror symmetry
, 2009
"... In this survey paper, we briefly review various aspects of the SYZ approach to mirror symmetry for nonCalabiYau varieties, focusing in particular on Lagrangian fibrations and wallcrossing phenomena in Floer homology. Various examples are presented, some of them new. ..."
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Cited by 24 (1 self)
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In this survey paper, we briefly review various aspects of the SYZ approach to mirror symmetry for nonCalabiYau varieties, focusing in particular on Lagrangian fibrations and wallcrossing phenomena in Floer homology. Various examples are presented, some of them new.
A counterexample to King’s conjecture
 Compos. Math
"... Abstract. King’s conjecture states that on every smooth complete toric variety X there exists a strongly exceptional collection which generates the bounded derived category of X and which consists of line bundles. We give a counterexample to this conjecture. This example is just the Hirzebruch surfa ..."
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Cited by 23 (4 self)
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Abstract. King’s conjecture states that on every smooth complete toric variety X there exists a strongly exceptional collection which generates the bounded derived category of X and which consists of line bundles. We give a counterexample to this conjecture. This example is just the Hirzebruch surface F2 iteratively blown up three times, and we show by explicit computation of cohomology vanishing that there exist no strongly exceptional sequences of length 7. 1.