A limit linear series moduli scheme

By Brian Osserman. 2004

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We develop a new, more functorial construction for the basic theory of limit linear series, which provides a compactification of the Eisenbud-Harris theory, and shows promise for generalization to higher-dimensional varieties and higher-rank vector bundles. We also give a result on lifting linear series from characteristic p to characteristic 0. In an appendix, in order to obtain the necessary dimensional lower bounds on our limit linear series scheme we develop a theory of "linked Grassmannians;" these are schemes parametrizing sub-bundles of a sequence of vector bundles which map into one another under fixed maps of the ambient bundles.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc227032cff8c676b3db5a5e11aeeb1e0294d8e8