Semiglobal results for $\overline \partial$ on complex spaces with arbitrary singularities, Part II
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- by Nils Øvrelid and Sophia Vassiliadou PDF
- Trans. Amer. Math. Soc. 363 (2011), 6177-6196 Request permission
Abstract:
We obtain some $L^2$-results for $\overline \partial$ 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 $L^2$-solvability results for compactly supported $\overline \partial$-closed $(p,q)$-forms $(0\le p\le n, 1\le q< n)$ on relatively compact subdomains $\Omega$ of the complex space that satisfy $H^{n-q}(\Omega , \mathcal {S})=0=H^{n-q+1}(\Omega , \mathcal {S})$ for every coherent $\mathcal {O}_X$-module $\mathcal {S}$. The latter result can be used to give an alternate proof of a theorem of Merker and Porten.References
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Additional Information
- Nils Øvrelid
- Affiliation: Department of Mathematics, University of Oslo, P.B. 1053 Blindern, Oslo, N-0316 Norway
- Email: nilsov@math.uio.no
- Sophia Vassiliadou
- Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057
- Email: sv46@georgetown.edu
- Received by editor(s): June 19, 2009
- Published electronically: July 14, 2011
- Additional Notes: The research of the second author was partially supported by NSF grant DMS-0712795
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 6177-6196
- MSC (2010): Primary 32B10, 32J25, 32W05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05274-8
- MathSciNet review: 2833549