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Tue, 09 Aug 2005 14:36:26 +0200Tue, 09 Aug 2005 14:36:26 +0200Maximal Cohen-Macaulay Modules over Two Cubic Hypersurface Singularities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1660
In the first part of this work, called Simple node singularity, are computed matrix factorizations of all isomorphism classes, up to shiftings, of rank one and two, graded, indecomposable maximal Cohen--Macaulay (shortly MCM) modules over the affine cone of the simple node singularity. The subsection 2.2 contains a description of all rank two graded MCM R-modules with stable sheafification on the projective cone of R, by their matrix factorizations. It is given also a general description of such modules, of any rank, over a projective curve of arithmetic genus 1, using their matrix factorizations. The non-locally free rank two MCM modules are computed using an alghorithm presented in the Introduction of this work, that gives a matrix factorization of any extension of two MCM modules over a hypersurface. In the second part, called Fermat surface, are classified all graded, rank two, MCM modules over the affine cone of the Fermat surface. For the classification of the orientable rank two graded MCM R-modules, is used a description of the orientable modules (over normal rings) with the help of codimension two Gorenstein ideals, realized by Herzog and Kühl. It is proven (in section 4), that they have skew symmetric matrix factorizations (over any normal hypersurface ring). For the classification of the non-orientable rank two MCM R-modules, we use a similar idea as in the case of the orientable ones, only that the ideal is not any more Gorenstein.Corina Baciudoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1660Thu, 08 Sep 2005 14:36:26 +0200Rank two Cohen-Macaulay modules over singularities of type .....
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1467
We describe, by matrix factoizations, all the rank two maximal Cohen-Macauly modules over singularities of type ......Corina Baciu; Vivian Ene; Gerhard Pfister; Dorin Popescupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1467Thu, 22 Jan 2004 10:18:48 +0100Maximal Cohen-Macaulay Modules over a Non-Isolated Hypersurface Singularity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1444
Corina Baciupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1444Mon, 03 Nov 2003 14:50:59 +0100