Browsing by Subject "Polynomial rings."

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    Free actions on CW-complexes and varieties of square zero matrices
    (2011) Şentürk, Berrin
    Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology over k. Carlsson showed that this conjecture implies the rank conjecture about free actions on product of spheres. In this paper, to understand the Carlsson’s conjecture about differential graded modules, we study the structure of the variety of upper triangular square zero matrices and the techniques which were investigated by Rothbach to determine its irreducible components . We hope these varieties could help prove Carlsson’s conjecture.
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    Invariant rings of modular P-groups
    (2013) Toper, Ceren Coşkun
    We consider a finite group acting as linear substitutions on a polynomial ring and study the corresponding ring of invariants. Computing the invariant ring and finding its ring theoretical properties is a classical problem. We focus on the modular case where the characteristic of the field divides the order of the group. We review invariants of basic modular actions and give explicit descriptions of invariants of small dimensional actions. We also discuss a recent algorithm that computes the invariant ring of a modular p-group up to a localization and we apply this algorithm to invariants of indecomposable representations of a cyclic group of prime order.