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Summary

In this chapter, we review the literature on interdependent routines. We group previous studies on routine interdependence around key concepts – boundaries & intersections, clusters, ecologies, and bundles – and highlight the different analytical foci and results of each group. Hence, we make an argument for leveraging the analytical differences of such concepts as cluster and ecologies, rather than treating them as synonyms. In closing, we point out several avenues for future research.

We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathcal{M}$ according to the Hilbert function H and classify all possible Hilbert functions H of such bundles. For each H, we describe a stratification of $\mathcal{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.

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Chapter 17 - Routine Interdependence

Summary

Bundles on $\textbf{P}^n$ with vanishing lower cohomologies

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Chapter 17 - Routine Interdependence

Summary

Bundles on $\textbf{P}^n$ with vanishing lower cohomologies