An infinite-dimensional N-graded k-algebra A is called projectively simple if dimk A/I < ∞ for every nonzero two-sided ideal I ⊂ A. We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring B = B(X,L, σ). Here X is a smooth projective variety, σ is an automorphis...

Let G be a finite group and k a field of characteristic p dividing |G|. Then Greenlees has developed a spectral sequence whose E2 term is the local cohomology of H∗(G, k) with respect to the maximal ideal, and which converges to H∗(G, k). Greenlees and Lyubeznik have used Grothendieck’s dual localization to provide a localized form of this spectral sequence with respect to a homogeneous prime i...

We intend to give a classification of smooth nondegenerate projective varieties admitting extremal or next to extremal curvilinear secant subspaces. Gruson, Lazarsfeld and Peskine classified all projective integral curves with extremal secant lines. On the other hand, if a locally Cohen-Macaulay variety Xn ⊂ Pn+e of degree d meets with a linear subspace L of dimension β at finite points, then l...

We investigate monomial labellings on cell complexes, giving a minimal cellular resolution of the ideal generated by these monomials, and such that the associated quotient ring is Cohen-Macaulay. We introduce a notion of such a labelling being maximal. There is only a finite number of maximal labellings for each cell complex, and we classify these for trees, partly for subdivisions of polygons,...

We consider the vertex-isoperimetric problem for cartesian powers of a graph G. A total order on the vertex set of G is called isoperimetric if the boundary of sets of a given size k is minimum for any initial segment of , and the ball around any initial segment is again an initial segment of . We prove a local-global principle with respect to the so-called simplicial order on Gn (see Section 2...