Nils Øvrelid

Solving on product singularities

Let X be a pure n-dimensional complex analytic set in with an isolated singularity at 0 and let Δ be the unit disk in centred at 0. We obtain some L 2-existence and regularity results for the -operator on the Cartesian product of a deleted neighbourhood of the singular point 0 in X with Δ.

LOCAL L2 RESULTS FOR

Let X be a reduced pure n-dimensional complex analytic set in ℂN with an isolated singularity at 0. We obtain some L2-existence and regularity results for the -operator on a deleted neighborhood of the singular point 0 in X.

\bar\partial

Let

: THE ISOLATED SINGULARITIES CASE

X

Some L 2 results for

be an irreducible

\overline\partial

n

on projective varieties with general singularities

-dimensional projective variety in

Semiglobal results for on a complex space with arbitrary singularities

{\Bbb C}P^N

L2-\overline{\partial}-Cohomology groups of some singular complex spaces

with arbitrary singular locus. We prove that the

Semiglobal results for \overline∂ on a complex space with arbitrary singularities

L^2