Dimension of linear systems: a combinatorial and differential approach
Abstract
We give upperbounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by AlexanderHirschowitz, 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.
 Publication:

arXiv eprints
 Pub Date:
 September 1997
 DOI:
 10.48550/arXiv.alggeom/9709032
 arXiv:
 arXiv:alggeom/9709032
 Bibcode:
 1997alg.geom..9032E
 Keywords:

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