Minimal free resolutions of fiber products

Minimal Free Resolutions of Homogenized D-modules

Strategies for Computing Minimal Free Resolutions

One of the most important computations in algebraic geometry or commutative algebra that a computer algebra system should provide is the computation of finite free resolutions of ideals and modules. Resolutions are used as an aid to understand the subtle nature of modules and are also a basis of further computations, such as computing sheaf cohomology, local cohomology, Ext, Tor, etc. Modern me...

MINIMAL FREE RESOLUTIONS over COMPLETE INTERSECTIONS

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...

Linear Free Resolutions and Minimal Multiplicity

Let S = k[x, ,..., x,] be a polynomial ring over a field and let A4 = @,*-a, M, be a finitely generated graded module; in the most interesting case A4 is an ideal of S. For a given natural number p, there is a great interest in the question: Can M be generated by (homogeneous) elements of degree <p? No simple answer, say in terms of the local cohomology of M, is known; but somewhat surprisingly...

Minimal Free Resolutions of Projective Subschemes of Small Degree

For an arbitrary projective subscheme X ⊂ P, it is impossible to say much about its minimal free resolution. Some a priori information is needed. In this article we will consider integral subschemes as well as equidimensional Cohen-Macaulay subschemes of small degree. There are several encouraging results for such subschemes in the literature. Our goal is to discuss the known results and to mot...