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• W1514271673 abstract "There are many examples of equivalences of triangulated categories $mathbf{D}^b(X) cong mathbf{D}^b(mathbf{A})$ where $X$ is a smooth quasi-projective variety and $mathbf{A}$ is an interesting abelian category. Viewing $mathbf{A}$ as a subcategory of $mathbf{D}^b(X)$, one would like to compare it to $mathbf{coh}(X)$. We consider tilting equivalences, Fourier-Mukai equivalences, and the McKay correspondence in dimension two (and three in the last case). In all three cases, we compute the relationship between $mathbf{coh}(X)$ and $mathbf{A}$ in a natural way in terms of slope stability and tilting. For surfaces admitting a tilting bundle, these considerations lead naturally to a criterion for rationality." @default.
• W1514271673 created "2016-06-24" @default.
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• W1514271673 date "2013-12-13" @default.
• W1514271673 modified "2023-09-27" @default.
• W1514271673 title "Derived equivalences of surfaces via numerical tilting" @default.
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• W1514271673 hasPublicationYear "2013" @default.
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