2024/03/01 by Nachiketa Adhikari, Yun Shi, Adhikari, Nachiketa +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2403.00727
openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that any (-2)-shifted symplectic derived scheme X (of finite type over an algebraically closed field of characteristic zero) is locally equivalent to the derived intersection of two Lagrangian morphisms to a (-1)-shifted symplectic derived scheme which is the (-1)-shifted cotangent stack of a smooth classical scheme. This leads to the possibility of the following viewpoint that is, at least to us, new: any n-shifted symplectic derived scheme can be obtained, locally, by repeated derived Lagrangian intersections in a smooth classical scheme. We also give a separate proof of our main result in the case where the local Darboux atlas cdga for X has an even number of generators in degree (-1); in this case we strengthen the result by showing that X is in fact locally equivalent to the derived critical locus of a shifted function, which we've been told is a folklore result in the field. We indicate the implications of this for derived moduli stacks of sheaves on Calabi-Yau fourfolds by spelling out the case when the fourfold is ℂ4.