Dimension of linear systems: a combinatorial and differential approach
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 1997
- DOI:
- 10.48550/arXiv.alg-geom/9709032
- arXiv:
- arXiv:alg-geom/9709032
- Bibcode:
- 1997alg.geom..9032E
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 17 pages, in french, also available at http://193.49.162.129/~evain/home.html