2018/12/02 by Tardini, Nicoletta
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1812.00362
We define the relative Dolbeault homology of a complex manifold with currents via a Čech approach and we prove its equivalence with the relative Čech-Dolbeault cohomology as defined in [T. Suwa, Čech-Dolbeault cohomology and the ∂-Thom class, \em Singularities---Niigata---Toyama 2007, 321--340, Adv. Stud. Pure Math., 56, Math. Soc. Japan, Tokyo, 2009. ]. This definition is then used to compare the relative Dolbeault cohomology groups of two complex manifolds of the same dimension related by a suitable proper surjective holomorphic map. Finally, an application to blow-ups is considered.