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 by Suwa (in: Singularities–Niigata–Toyama 2007. Advanced studies in pure mathematics, vol 56. Mathematical Society of Japan, Tokyo, pp 321–340, 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 and a blow-up formula for the Dolbeault cohomology in terms of relative cohomology is presented.

Relative Čech–Dolbeault homology and applications / Tardini, N.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:3(2020), pp. 985-995. [10.1007/s10231-019-00909-x]

Relative Čech–Dolbeault homology and applications

Tardini N.
2020

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 by Suwa (in: Singularities–Niigata–Toyama 2007. Advanced studies in pure mathematics, vol 56. Mathematical Society of Japan, Tokyo, pp 321–340, 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 and a blow-up formula for the Dolbeault cohomology in terms of relative cohomology is presented.
Relative Čech–Dolbeault homology and applications / Tardini, N.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:3(2020), pp. 985-995. [10.1007/s10231-019-00909-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2880344
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