Dimension of linear systems: a combinatorial and differential approach

Details Dimension of linear systems: a combinatorial and differential approach Dimension of linear systems: a combinatorial and differential approach

1997-09-29

arxiv.org/abs/alg-geom/9709032v1

Mathematics

Algebraic Geometry

17 pages, in french, also available at http://193.49.162.129/~evain/home.html

Scientific paper

We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension of linear systems of hypersurfaces in a projective space $\PP^n$ with generically prescribed singularities, and the calculus of collisions of fat points in $\PP^2$. These applications will be treated independently but a simple example in the introduction explains how the theorem will be used.

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