561 research outputs found
-theory for the -operator on compact complex spaces
Let be a singular Hermitian complex space of pure dimension . We use a
resolution of singularities to give a smooth representation of the
--cohomology of -forms on . The central tool
is an -resolution for the Grauert-Riemenschneider canonical sheaf
. As an application, we obtain a Grauert-Riemenschneider-type
vanishing theorem for forms with values in almost positive line bundles. If
is a Gorenstein space with canonical singularities, then we get also an
-representation of the flabby cohomology of the structure sheaf
. To understand also the --cohomology of
-forms on , we introduce a new kind of canonical sheaf, namely the
canonical sheaf of square-integrable holomorphic -forms with some
(Dirichlet) boundary condition at the singular set of . If has only
isolated singularities, then we use an -resolution for that sheaf and a
resolution of singularities to give a smooth representation of the
--cohomology of -forms.Comment: 34 page
Koppelman formulas on the A_1-singularity
In the present paper, we study the regularity of the Andersson-Samuelsson
Koppelman integral operator on the -singularity. Particularly, we prove
- and -estimates. As applications, we obtain -homotopy formulas
for the -equation on the -singularity, and we prove that
the -forms introduced by Andersson-Samuelsson are continuous on
the -singularity.Comment: 23 pages. v3: Minor changes made for the final versio
Modifications of torsion-free coherent analytic sheaves
We study the transformation of torsion-free coherent analytic sheaves under
proper modifications. More precisely, we study direct images of inverse image
sheaves, and torsion-free preimages of direct image sheaves. Under some
conditions, it is shown that torsion-free coherent sheaves can be realized as
the direct image of locally free sheaves under modifications. Thus, it is
possible to study coherent sheaves modulo torsion by reducing the problem to
study vector bundles on manifolds. We apply this to reduced ideal sheaves and
to the Grauert-Riemenschneider canonical sheaf of holomorphic n-forms.Comment: 28 pages; the article has been completely rewritten due to a wrong
statement in the first versio
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