2023/09/06 by Michail Savvas, Savvas, Michail
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2309.03066
openalex publication_date 2023/09/06 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28
This is a continuation of prior work of the author on cosection localization for d-manifolds. We construct reduced virtual fundamental classes for derived manifolds with surjective cosections and cosection localized virtual fundamental classes for (-2)-shifted symplectic derived schemes in larger generality. Moreover, using recent results of Oh-Thomas, we show that the algebraic and differential geometric constructions of reduced and cosection localized virtual fundamental classes of (-2)-shifted symplectic derived schemes yield the same result in homology. We obtain applications towards the construction and integrality of reduced invariants in Donaldson-Thomas theory of Calabi-Yau fourfolds.