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Zur Hilbert-Funktion by Berman, Aaron

Zur Hilbert-Funktion

by Aaron Berman
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Book cover type: Paperback
  • ISBN13: 9783668791046
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 44
  • Original Price: USD 25.5
  • Language: German
  • Edition: 1. Auflage
  • Item Weight: 68 grams
  • BISAC Subject(s): Algebra / General

Bachelorarbeit aus dem Jahr 2016 im Fachbereich Mathematik - Algebra, Note: 1, Johann Wolfgang Goethe-Universität Frankfurt am Main, Sprache: Deutsch, Abstract: Die Hilbert-Funktion, zumindest so weit, wie ich sie hier behandeln werde, misst die Vektorraumdimension der verschiedenen Stückchen graduierter Moduln. Dabei stellte bereits Hilbert beeindruckenderweise fest, dass diese Funktion von polynomiellem Typ ist, also dass für gross genuge Argumente, diese Hilbert-Funktion mit einem Polynom übereinstimmt. Die Hilbert-Funktion hat dabei eine Grosszahl an Anwendungen und Verstrickungen mit Fragestellungen der kommutativen Algebra und ich stellte bei der Bearbeitung des Themas schnell fest, dass eine Einschränkung notwendig sein würde und ich selbst in diesem eingeschränkten Teilbereich zu gro en Teilen nur einen Geschmack der Möglichkeiten der Hilbert-Funktion vermitteln können würde. Anstatt etwa auf die kombinatorischen Anwendungen auf Simplizialkomplexen oder die leichte Berechnbarkeit durch Gröbner Basen einzugehen, die beide bestimmt auch wesentlich für ihre Attraktivität sind, entschied ich mich zur Beschäftigung mit geometrischen Fragen. Diese drehen sich hauptsächlich um Varietäten im projektiven Raum.

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