Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds
We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules with coherent cohomology, by means of the DG-category of $\bar\partial$-superconnections. Then we apply the techniques of $\bar\partial$-superc...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Bondal, Alexey Rosly, Alexei |
| description | We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm
coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules
with coherent cohomology, by means of the DG-category of
$\bar\partial$-superconnections. Then we apply the techniques of
$\bar\partial$-superconnections to define Chern classes and Bott-Chern classes
of objects in the category, in particular, of coherent sheaves. |
| doi_str_mv | 10.48550/arxiv.2211.11112 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2211_11112</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2211_11112</sourcerecordid><originalsourceid>FETCH-LOGICAL-a672-76c50050c2549061edcd19f774b16141ae3f640cf40d2bffb5be32376fa45fcb3</originalsourceid><addsrcrecordid>eNotj8tqwzAURLXpoiT9gK6qD6hdvZUsg-kLErpIdl2Ya_mKGBTJWG5I_r6O29kMMwwDh5BHzkq10pq9wHDpzqUQnJd8krgn31U64oBxpPsjwhnzM62mItIqQM63CLGl-58eB5diRDd2KWaapkE69eDG2QNeik2EcB07R3cQO59Cm5fkzkPI-PDvC3J4ez1UH8X26_2z2mwLMFYU1jjNmGZOaLVmhmPrWr721qqGG644oPRGMecVa0XjfaMblEJa40Fp7xq5IE9_tzNd3Q_dCYZrfaOsZ0r5C8qnTXQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds</title><source>arXiv.org</source><creator>Bondal, Alexey ; Rosly, Alexei</creator><creatorcontrib>Bondal, Alexey ; Rosly, Alexei</creatorcontrib><description>We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm
coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules
with coherent cohomology, by means of the DG-category of
$\bar\partial$-superconnections. Then we apply the techniques of
$\bar\partial$-superconnections to define Chern classes and Bott-Chern classes
of objects in the category, in particular, of coherent sheaves.</description><identifier>DOI: 10.48550/arxiv.2211.11112</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2022-11</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/2211.11112$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2211.11112$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bondal, Alexey</creatorcontrib><creatorcontrib>Rosly, Alexei</creatorcontrib><title>Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds</title><description>We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm
coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules
with coherent cohomology, by means of the DG-category of
$\bar\partial$-superconnections. Then we apply the techniques of
$\bar\partial$-superconnections to define Chern classes and Bott-Chern classes
of objects in the category, in particular, of coherent sheaves.</description><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwzAURLXpoiT9gK6qD6hdvZUsg-kLErpIdl2Ya_mKGBTJWG5I_r6O29kMMwwDh5BHzkq10pq9wHDpzqUQnJd8krgn31U64oBxpPsjwhnzM62mItIqQM63CLGl-58eB5diRDd2KWaapkE69eDG2QNeik2EcB07R3cQO59Cm5fkzkPI-PDvC3J4ez1UH8X26_2z2mwLMFYU1jjNmGZOaLVmhmPrWr721qqGG644oPRGMecVa0XjfaMblEJa40Fp7xq5IE9_tzNd3Q_dCYZrfaOsZ0r5C8qnTXQ</recordid><startdate>20221120</startdate><enddate>20221120</enddate><creator>Bondal, Alexey</creator><creator>Rosly, Alexei</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221120</creationdate><title>Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds</title><author>Bondal, Alexey ; Rosly, Alexei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-76c50050c2549061edcd19f774b16141ae3f640cf40d2bffb5be32376fa45fcb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Bondal, Alexey</creatorcontrib><creatorcontrib>Rosly, Alexei</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bondal, Alexey</au><au>Rosly, Alexei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds</atitle><date>2022-11-20</date><risdate>2022</risdate><abstract>We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm
coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules
with coherent cohomology, by means of the DG-category of
$\bar\partial$-superconnections. Then we apply the techniques of
$\bar\partial$-superconnections to define Chern classes and Bott-Chern classes
of objects in the category, in particular, of coherent sheaves.</abstract><doi>10.48550/arxiv.2211.11112</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2211.11112 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2211_11112 |
| source | arXiv.org |
| subjects | Mathematics - Algebraic Geometry |
| title | Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-22T20%3A12%3A02IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Coherent%20Sheaves,%20Chern%20Classes,%20and%20Superconnections%20on%20Compact%20Complex-Analytic%20Manifolds&rft.au=Bondal,%20Alexey&rft.date=2022-11-20&rft_id=info:doi/10.48550/arxiv.2211.11112&rft_dat=%3Carxiv_GOX%3E2211_11112%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |