We review the derived algebraic geometry of derived zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we some of the structures carried by derived critical loci: the homotopy Batalin-Vilkovisky structure, the action of the 2-monoid of the self-intersection of the zero section, and the derived symplectic structure of degree -1. We also show how this structure exists, more generally, on derived lagrangian intersections inside a symplectic algebraic manifold.
Basic structures on derived critical loci / Vezzosi Gabriele. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - Special issue on Geometry of PDEs' - In memory of Alexandre Mikhailovich Vinogradov:(2020), pp. 1-11. [10.1016/j.difgeo.2020.101635]
Basic structures on derived critical loci
Vezzosi Gabriele
2020
Abstract
We review the derived algebraic geometry of derived zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we some of the structures carried by derived critical loci: the homotopy Batalin-Vilkovisky structure, the action of the 2-monoid of the self-intersection of the zero section, and the derived symplectic structure of degree -1. We also show how this structure exists, more generally, on derived lagrangian intersections inside a symplectic algebraic manifold.File | Dimensione | Formato | |
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