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Nils Ovrelid

Publications and source records attributed to Nils Ovrelid.

6 recordsLinked to original sources
arXiv2011

L2 d-bar cohomology groups of some singular complex spaces

Let X be a pure n-dimensional (n>1) complex analytic set in C^N with an isolated singularity at 0. In this paper we express the L2-(0,q)-d-bar-cohomology groups for all q with 0<q<n+1, of a sufficiently small deleted neighborhood of the singular point, in terms of resolution data. We also obtain identifications of the L2-(0,q)-d-bar-cohomology groups of the smooth points of X in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities.

math.CV↗
arXiv2009

Hartogs' extension theorems on Stein spaces

We discuss various known generalizations of the classical Hartogs' extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on d-bar methods.

math.CV↗
arXiv2009

Semiglobal results for d-bar on complex spaces with arbitrary singularities, Part II

We obtain some L2 results for d-bar on forms that vanish to high order on the singular set of a complex space. As a consequence of our main theorem we obtain weighted L2-solvability results for compactly supported d-bar closed (p,q) forms defined on certain relatively compact subdomains of the complex space. The latter result can be used to give an alternate proof of a theorem of Merker and Porten.

math.CV↗