K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

Using projective techniques to tap into consumers' feelings, perceptions and attitudes ... getting an honest opinion

An investigation into customer loyalty to food retailers posed a methodological problem namely how to delve beneath the surface and access consumers' unspoken feelings, perceptions, attitudes and values. This paper explains how four different projective techniques were used to access the thoughts and feelings of 160 interviewees in order to obtain a thorough understanding of the interviewees' satisfaction with their 'main' food retailer and to characterize the relationship between the customer and retailer. A brief description of the use, analysis and examples of cartoon friends, word association, personification and mini case studies was provided in order to describe their role in the data collection process.

A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.