2020/10/27 by Albin Grataloup, Grataloup, Albin
Mathematics · #14A30 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2010.14221
openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the symplectic geometry of derived intersections of Lagrangian morphisms. In particular, we show that for a functional f : X → \mathbbAk1, the derived critical locus has a natural Lagrangian fibration Crit(f) → X. In the case where f is non-degenerate and the strict critical locus is smooth, we show that the Lagrangian fibration on the derived critical locus is determined by the Hessian quadratic form.