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arXiv · 1812.00362

Relative Čech-Dolbeault homology and applications

Nicoletta Tardini
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Abstract

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 $\overline\partial$-Thom class, {\em Singularities---Niigata---Toyama 2007}, 321--340, Adv. Stud. Pure Math., \textbf{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.

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Nicoletta Tardini. 2019-06-10. Relative Čech-Dolbeault homology and applications. https://arxiv.org/abs/1812.00362

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