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arXiv · 1509.06174

On the $L^2$-$\overline{\partial}$-cohomology of certain complete Kähler metrics

Francesco Bei·Paolo Piazza
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Abstract

Let $V$ be a compact and irreducible complex space of complex dimension $v$ whose regular part is endowed with a complete Hermitian metric $h$. Let $π:M\rightarrow V$ be a resolution of $V$. Under suitable assumptions on $h$ we prove that $$H^{v,q}_{2,\overline{\partial}}(\operatorname{reg}(V),g)\cong H^{v,q}_{\overline{\partial}}(M),\ q=0,...,v.$$ Then we show that the previous isomorphism applies to the case of Saper-type Kähler metrics and to the case of complete Kähler metrics with finite volume and pinched negative sectional curvatures.

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Francesco Bei, Paolo Piazza. 2017-12-19. On the $L^2$-$\overline{\partial}$-cohomology of certain complete Kähler metrics. https://arxiv.org/abs/1509.06174

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