The Ideal Generation Problem for Fat Points
Abstract
This paper is concerned with determining the number of generators in each degree for minimal sets of homogeneous generators for saturated ideals defining fat point subschemes $Z=m_1p_1+ ... +m_rp_r$ for general sets of points $p_i$ of $P^2$. For thin points (i.e., m_i=1 for all i), a solution is known, in terms of a maximal rank property. Although this property in general fails for fat points, we show it holds in an appropriate asymptotic sense. In the uniform (i.e., $m_1= ... =m_r$) case, we determine all failures of this maximal rank property for $r\le 9$, and we develop evidence for the conjecture that no other failures occur for $r > 9$.
 Publication:

arXiv eprints
 Pub Date:
 March 1997
 DOI:
 10.48550/arXiv.alggeom/9703035
 arXiv:
 arXiv:alggeom/9703035
 Bibcode:
 1997alg.geom..3035H
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 PlainTeX, 17 pages