Publikation:

Homology and Cohomology of Toric Varieties

Lade...
Vorschaubild

Dateien

preprint_057.pdf
preprint_057.pdfGröße: 1.34 MBDownloads: 1099

Datum

1998

Autor:innen

Jordan, Arno

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Auflagebezeichnung

DOI (zitierfähiger Link)
ArXiv-ID

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung
Open Access Green
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Preprint
Publikationsstatus
Published

Erschienen in

Zusammenfassung

By the Theorem of Jurkiewicz-Danilov, there is an isomorphism of graded rings between the integral cohomology ring and the Chow ring of a "smooth" compact toric variety; moreover, an explicit computation of both rings is provided with the help of the finitely many integral data encoded in the fan that defines the toric variety. As a generalization to even noncompact toric varieties with arbitrary singularities, we show the following:

There is a spectral sequence - induced by the orbit structure - that converges to the integral (resp. rational) homology with closed supports of such a toric variety, where the Chow groups appear as the diagonal E2-terms. In addition, for homology with closed supports and coefficients in an abelian group, the homology groups in low and in high degrees of any toric variety are explicitly computed.

Finally, we develop the dual theory for cohomology with compact supports and coefficients in an abelian group, generalizing Fischli's approach and results for the computation of the integral cohomology of compact toric varieties.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
004 Informatik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690JORDAN, Arno, 1998. Homology and Cohomology of Toric Varieties
BibTex
@unpublished{Jordan1998Homol-6176,
  year={1998},
  title={Homology and Cohomology of Toric Varieties},
  author={Jordan, Arno},
  note={Buchhandelsausg. erschienen 1998 im Verl. Hartung-Gorre, Konstanz. ISBN 3-89649-273-X}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/6176">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:09:58Z</dcterms:available>
    <dcterms:title>Homology and Cohomology of Toric Varieties</dcterms:title>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/6176/1/preprint_057.pdf"/>
    <dcterms:issued>1998</dcterms:issued>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/6176/1/preprint_057.pdf"/>
    <dc:language>eng</dc:language>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Jordan, Arno</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T16:09:58Z</dc:date>
    <dc:format>application/pdf</dc:format>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/6176"/>
    <dcterms:abstract xml:lang="eng">By the Theorem of Jurkiewicz-Danilov, there is an isomorphism of graded rings between the integral cohomology ring and the Chow ring of a "smooth" compact toric variety; moreover, an explicit computation of both rings is provided with the help of the finitely many integral data encoded in the fan that defines the toric variety. As a generalization to even noncompact toric varieties with arbitrary singularities, we show the following:&lt;br /&gt;&lt;br /&gt;There is a spectral sequence - induced by the orbit structure - that converges to the integral (resp. rational) homology with closed supports of such a toric variety, where the Chow groups appear as the diagonal E2-terms. In addition, for homology with closed supports and coefficients in an abelian group, the homology groups in low and in high degrees of any toric variety are explicitly computed.&lt;br /&gt;&lt;br /&gt;Finally, we develop the dual theory for cohomology with compact supports and coefficients in an abelian group, generalizing Fischli's approach and results for the computation of the integral cohomology of compact toric varieties.</dcterms:abstract>
    <dc:contributor>Jordan, Arno</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Buchhandelsausg. erschienen 1998 im Verl. Hartung-Gorre, Konstanz. ISBN 3-89649-273-X
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Begutachtet
Diese Publikation teilen