Essential normality of quotient submodules over strongly pseudoconvex finite manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929348839211008 |
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| author | Ding, Lijia |
| author_facet | Ding, Lijia |
| contents | We investigate the $p$-essential normality of Hilbert quotient submodules on a relatively compact smooth strongly pseudoconvex domain in a complex manifold satisfying Property (S). For analytic subvarieties that have compact singularities and transversely intersect the strongly pseudoconvex boundary, we prove that the corresponding Bergman-Sobolev quotient submodules are $p$-essentially normal whenever $p$ exceeds the dimension of the noncompact part of the analytic subvarieties. As a consequence, we partially confirm the geometric Arveson-Douglas Conjecture and resolve an open problem regarding the trace-class antisymmetric sum of truncated Toeplitz operators within a broader context. Moreover, we provide applications in $K$-homology and geometric invariant theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Essential normality of quotient submodules over strongly pseudoconvex finite manifolds Ding, Lijia Complex Variables 46H25, 47A13, 32Q28, 19K56 We investigate the $p$-essential normality of Hilbert quotient submodules on a relatively compact smooth strongly pseudoconvex domain in a complex manifold satisfying Property (S). For analytic subvarieties that have compact singularities and transversely intersect the strongly pseudoconvex boundary, we prove that the corresponding Bergman-Sobolev quotient submodules are $p$-essentially normal whenever $p$ exceeds the dimension of the noncompact part of the analytic subvarieties. As a consequence, we partially confirm the geometric Arveson-Douglas Conjecture and resolve an open problem regarding the trace-class antisymmetric sum of truncated Toeplitz operators within a broader context. Moreover, we provide applications in $K$-homology and geometric invariant theory. |
| title | Essential normality of quotient submodules over strongly pseudoconvex finite manifolds |
| topic | Complex Variables 46H25, 47A13, 32Q28, 19K56 |
| url | https://arxiv.org/abs/2405.11929 |