2024/04/15 by Zhaobo, Han, Zhaobo Tom
Materials Science · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #High voltage insulation and dielectric phenomena
paper · pdf · doi:10.48550/arxiv.2404.09439
openalex publication_date 2024/04/15 · openalex created_date 2024/04/17 · openalex updated_date 2026/07/28
Let F be a coherent sheaf on a complex variety X that has a locally free resolution E\bullet. In [19], the authors constructed a pseudomeromorphic current whose support is contained in supp(E\bullet) that represents products of Chern classes of F. In this paper, we show that their construction works for general de-Rham characteristic classes and then generalize it to represent products (in de-Rham cohomology) of characteristic forms of cohesive modules defined by Block. Finally, we state a corollary to a transgression result in [16] that show that it is sufficient to only use the degree-0 and degree-1 parts of the superconnection to construct currents that represent characteristic forms of cohesive modules in the Bott-Chern cohomology.