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Showing 1 to 4 of 4 for “"hypersurface ring"”.
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Homology over a Complete Intersection Ring via the Generic Hypersurface
… for modules over a complete intersection ring $Q/(f_1,\ldots,f_c)$ by way of the related generic hypersurface ring $Q[T_1,\ldots,T_c]/(f_1T_1+\cdots+f_cT_c)$. The advantage of this approach is that over a hypersurface ring, free resolutions are eventually 2-periodic, given by matrix …
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The syzygy theorem and the weak Lefschetz Property
… of linear forms in a standard graded polynomial ring of characteristic zero. The main point to take away from these developments is that, via the inverse system dictionary, one is able to relate the failure of the Weak Lefschetz property to the geometry of the fat point scheme associated to the …
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Matrix Factorizations With More Than Two Factors
<p>Let $S$ be a regular local ring and $f$ a non-zero non-invertible element of $S$. In this thesis, we study the notion of a matrix factorization of $f$ with $d\ge 2$ factors, that is, we consider tuples of square matrices $(\phi_1,\phi_2,\dots,\phi_d)$, with entries in $S$, such that their …
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Weak Purity for Gorenstein Rings
… branch locus theorem states that a module finite ring extension of local normal domains $B\to A$ which is unramified in codimension one, with B a regular local ring, is unramified (and in this setting, etale). When the ring B is merely Gorenstein, there are numerous examples which show that A need …