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arXiv · alg-geom/9709032

Dimension of linear systems: a combinatorial and differential approach

L. Evain
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Abstract

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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L. Evain. 1997-09-29. Dimension of linear systems: a combinatorial and differential approach. https://arxiv.org/abs/alg-geom/9709032

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