Now showing items 51-52 of 52
Generalized Involutive Bases and Their Induced Free Resolutions
In this thesis, we generalize several types of involutive and marked bases for ideals in quotient rings of commutative polynomial rings. We apply these new types of bases to the analysis of infinite free resolutions and of Hilbert schemes defined over certain types of quotient rings. We are mostly concerned with Pommaret and Janet bases; the marked bases we consider are marked over monomial submodules that are quasi-stable, i.e., that possess finite Pommaret bases. Involutive bases of the types we consider induce ...
Free Resolutions from Involutive Bases
We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the ...