Global ETD Search

1	Dagger closure Stäbler, Axel 17 January 2011 (has links) We prove that solid closure and graded dagger closure agree for homogeneous ideals in two dimensional $\mathbb{N}$-graded domains of finite type over a field. We also prove that dagger closure is trivial for ideals in regular rings containing a field and that graded dagger closure is trivial for $\mathbb{N}$-graded regular rings of finite type over a field. Finally, we prove an inclusion result for graded dagger closure for homogeneous primary ideals in certain section rings of abelian varieties. Idealabschlussoperation 31.23 - Ideale, Ringe, Moduln, Algebren 31.51 - Algebraische Geometrie 14-02 - Research exposition 13-02 - Research exposition ddc:510
2	Ideal Closures and Sheaf Stability Steinbuch, Jonathan 20 January 2021 (has links) The two main parts of this doctoral thesis are a theorem that tight closure is contained in continuous closure via axes closure on the one hand and an algorithm to decide semistability of sheaves (or geometric vector bundles) via reduction to a linear algebra problem on the other hand. The sheaf stability algorithm was explicitly implemented by the author. sheaf stability ideal closures computer algebra tight closure stable vector bundles 31.51 - Algebraische Geometrie 31.23 - Ideale, Ringe, Moduln, Algebren ddc:510
3	Hilbert-Kunz functions of surface rings of type ADE / Hilbert-Kunz Funktionen zweidimensionaler Ringe vom Typ ADE Brinkmann, Daniel 27 August 2013 (has links) We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals. Hilbert-Kunz ADE singularity maximal Cohen-Macaulay vector bundle Frobenius periodicity Hilbert-series syzygy module matrix factorization Fermat curve strongly semistable 31.51 - Algebraische Geometrie 31.23 - Ideale, Ringe, Moduln, Algebren ddc:510

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