On $k$-Du Bois and $k$-rational singularities
We introduce new notions of $k$-Du Bois and $k$-rational singularities, extending the previous definitions in the case of local complete intersections (lci), to include natural examples outside of this setting. We study the stability of these notions under general hyperplane sections and show that v...
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| creator | Shen, Wanchun Venkatesh, Sridhar Vo, Anh Duc |
| description | We introduce new notions of $k$-Du Bois and $k$-rational singularities,
extending the previous definitions in the case of local complete intersections
(lci), to include natural examples outside of this setting. We study the
stability of these notions under general hyperplane sections and show that
varieties with $k$-rational singularities are $k$-Du Bois, extending previous
results in [MP22b] and [FL22b] in the lci and the isolated singularities cases.
In the process, we identify the aspects of the theory that depend only on the
vanishing of higher cohomologies of Du Bois complexes (or related objects), and
not on the behaviour of the K\"ahler differentials. |
| doi_str_mv | 10.48550/arxiv.2306.03977 |
| format | Article |
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extending the previous definitions in the case of local complete intersections
(lci), to include natural examples outside of this setting. We study the
stability of these notions under general hyperplane sections and show that
varieties with $k$-rational singularities are $k$-Du Bois, extending previous
results in [MP22b] and [FL22b] in the lci and the isolated singularities cases.
In the process, we identify the aspects of the theory that depend only on the
vanishing of higher cohomologies of Du Bois complexes (or related objects), and
not on the behaviour of the K\"ahler differentials.</description><identifier>DOI: 10.48550/arxiv.2306.03977</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2023-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2306.03977$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2306.03977$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Shen, Wanchun</creatorcontrib><creatorcontrib>Venkatesh, Sridhar</creatorcontrib><creatorcontrib>Vo, Anh Duc</creatorcontrib><title>On $k$-Du Bois and $k$-rational singularities</title><description>We introduce new notions of $k$-Du Bois and $k$-rational singularities,
extending the previous definitions in the case of local complete intersections
(lci), to include natural examples outside of this setting. We study the
stability of these notions under general hyperplane sections and show that
varieties with $k$-rational singularities are $k$-Du Bois, extending previous
results in [MP22b] and [FL22b] in the lci and the isolated singularities cases.
In the process, we identify the aspects of the theory that depend only on the
vanishing of higher cohomologies of Du Bois complexes (or related objects), and
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extending the previous definitions in the case of local complete intersections
(lci), to include natural examples outside of this setting. We study the
stability of these notions under general hyperplane sections and show that
varieties with $k$-rational singularities are $k$-Du Bois, extending previous
results in [MP22b] and [FL22b] in the lci and the isolated singularities cases.
In the process, we identify the aspects of the theory that depend only on the
vanishing of higher cohomologies of Du Bois complexes (or related objects), and
not on the behaviour of the K\"ahler differentials.</abstract><doi>10.48550/arxiv.2306.03977</doi><oa>free_for_read</oa></addata></record> |
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| title | On $k$-Du Bois and $k$-rational singularities |
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