Free Factorizations
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Matrix Factorizations for Complete Intersections and Minimal Free Resolutions
Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface, and also define a functor to the stable module category of maximal Cohen-Macaulay modules on the hypersurface. We introduce a new functorial concept of matrix factorizations for complete intersections that allows us to describe the asymptotic structure of mi...
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We begin the chapter with some history of the results that form the background of this book. We then define higher matrix factorizations, our main focus. While classical matrix factorizations were factorizations of a single element, higher matrix factorizations deal directly with sequences of elements. In section 1.3, we outline our main results. Throughout the book, we use the notation introdu...
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Let M(A, θ) be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet B ⊂ A such that the right factor of a bisection M(A, θ) = M(B, θB).T be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of M(A, θ) and associated bases of LK(A, θ).
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