Homological mirror symmetry is T-duality for $\mathbb P^n$

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dc.creatorFang, Bohan
dc.date2008-04-04
dc.date2008-10-29
dc.date.accessioned2026-07-07T10:13:32Z
dc.date.available2026-07-07T10:13:32Z
dc.descriptionIn this paper, we apply the idea of T-duality to projective spaces. From a connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror Landau-Ginzburg model is constructed. Under this correspondence, the full strong exceptional collection $\mathcal O_{\mathbb P^n}(-n-1),...,\mathcal O_{\mathbb P^n}(-1)$ is mapped to standard Lagrangians in the sense of \cite{nz}. Passing to constructible sheaves, we explicitly compute the quiver structure of these Lagrangians, and find that they match the quiver structure of this exceptional collection of $\mathbb P^n$. In this way, T-duality provides quasi-equivalence of the Fukaya category generated by these Lagrangians and the category of coherent sheaves on $\mathbb P^n$, which is a kind of homological mirror symmetry.
dc.description21 pages, 4 figures, submitted version
dc.identifierhttps://arxiv.org/abs/0804.0646
dc.identifierhttp://arxiv.org/abs/0804.0646
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172561
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.titleHomological mirror symmetry is T-duality for $\mathbb P^n$
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