A Lower Bound for the Determinantal Complexity of a Hypersurface View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-06

AUTHORS

Jarod Alper, Tristram Bogart, Mauricio Velasco

ABSTRACT

We prove that the determinantal complexity of a hypersurface of degree d>2 is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the 3×3 permanent is 7. We also prove that for n>3, there is no nonsingular hypersurface in Pn of degree d that has an expression as a determinant of a d×d matrix of linear forms, while on the other hand for n≤3, a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5. More... »

PAGES

829-836

References to SciGraph publications

  • 1998-09. Parametrization of the orbits of cubic surfaces in TRANSFORMATION GROUPS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10208-015-9300-x

    DOI

    http://dx.doi.org/10.1007/s10208-015-9300-x

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