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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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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 investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the LandauGinzburg model. 1.
doi:10.1093/imrn/rnu072 Categorical Resolutions of Irrational Singularities
"... We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category that has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical res ..."
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We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category that has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity. 1
GENERATING THE BOUNDED DERIVED CATEGORY AND PERFECT GHOSTS
"... Abstract. We show, for a wide class of abelian categories relevant in representation theory and algebraic geometry, that the bounded derived categories have no nontrivial strongly finitely generated thick subcategories containing all perfect complexes. In order to do so we prove a strong converse ..."
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Abstract. We show, for a wide class of abelian categories relevant in representation theory and algebraic geometry, that the bounded derived categories have no nontrivial strongly finitely generated thick subcategories containing all perfect complexes. In order to do so we prove a strong converse of the Ghost Lemma for bounded derived categories. 1.
Categorical resolutions, poset schemes and Du Bois singularities, preprint arXiv:1011.6089
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