2011/09/23 by Gabriele Vezzosi, Vezzosi, Gabriele · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG
paper · pdf · doi:10.48550/arxiv.1109.5213
Notes
arxiv created 2011/09/23 · openalex publication_date 2011/09/23 · arxiv updated 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will quickly explore the derived geometry of zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we will single out many of the derived geometric 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, and show how this structure exists, more generally, on derived lagrangian intersections inside a symplectic manifold. These are just applications of a small part of a much larger project - joint with Pantev, Toën and Vaquié - investigating quantization of derived moduli spaces.