2025/04/28 by Young‐Hoon Kiem, Kiem, Young-Hoon, Hyeonjun Park +1 · 2 citations
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
paper · pdf · doi:10.48550/arxiv.2504.19542
openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to shed a new light on classical constructions in enumerative geometry from the view point of derived algebraic geometry. We first prove that the cosection localized virtual cycle of a quasi-smooth derived Deligne-Mumford stack with a (-1)-shifted closed 1-form is equal to the virtual Lagrangian cycle of the degeneracy locus which is (-2)-shifted symplectic. We next establish a shifted analogue of the Lagrange multipliers method which gives us the quantum Lefschetz theorems as immediate consequences of the equality of virtual cycles. Lastly we study derived algebraic geometry enhancements of gauged linear sigma models which lead us to the relative virtual cycles in a general and natural form.