Some L 2 results for $\overline\partial$ on projective varieties with general singularities
Let $X$ be an irreducible $n$-dimensional projective variety in ${\Bbb C}P^N$ with arbitrary singular locus. We prove that the $L^2$-$\overline\partial$-$(p,1)$-cohomology groups (with respect to the Fubini-Study metric) of the regular part of $X$ are finite dimensional.
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| Veröffentlicht in: | American journal of mathematics 2009-02, Vol.131 (1), p.129-151 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let $X$ be an irreducible $n$-dimensional projective variety in ${\Bbb C}P^N$
with arbitrary singular locus. We prove that the
$L^2$-$\overline\partial$-$(p,1)$-cohomology groups (with respect to the
Fubini-Study metric) of the regular part of $X$ are finite dimensional. |
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| ISSN: | 1080-6377 1080-6377 |
| DOI: | 10.1353/ajm.0.0037 |