A limit linear series moduli scheme

Details A limit linear series moduli scheme A limit linear series moduli scheme

2004-07-28

arxiv.org/abs/math/0407496v1

Mathematics

Algebraic Geometry

30 pages. Contents of chapter II of PhD thesis, Massachusetts Institute of Technology, 2004

Scientific paper

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.

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