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  <doc>
    <id>8084</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>35</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>555</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hypersurfaces with defect</title>
    <abstract language="eng">A projective hypersurface X⊆P^n has defect if h^i(X) ≠ h^i(P^n) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P^4 is not Q-factorial. We show that hypersurfaces with defect tend to be very singular: In characteristic 0, we present a lower bound on the Tjurina number, where X is allowed to have arbitrary isolated singularities. For X with mild singularities, we prove a similar result in positive characteristic. As an application, we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field.</abstract>
    <parentTitle language="eng">Journal of Algebra</parentTitle>
    <identifier type="doi">10.1016/j.jalgebra.2020.02.022</identifier>
    <identifier type="arxiv">1610.04077</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Niels Lindner</author>
    <submitter>Niels Lindner</submitter>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="projects" number="ECMath-MI7">ECMath-MI7</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
  </doc>
</export-example>
