Degenerations of Planar Linear Systems
| dc.creator | Ciliberto, C. | |
| dc.creator | Miranda, R. | |
| dc.date | 1997-02-21 | |
| dc.date | 1998-04-03 | |
| dc.date.accessioned | 2026-07-07T09:01:49Z | |
| dc.date.available | 2026-07-07T09:01:49Z | |
| dc.description | Fixing $n$ general points $p_i$ in the plane, what is the dimension of the space of plane curves of degree $d$ having multiplicity $m_i$ at $p_i$ for each $i$? In this article we propose an approach to attack this problem, and demonstrate it by successfully computing this dimension for all $n$ and for $m_i$ constant, at most 3. This application, while previously known (see \cite{hirschowitz1}), demonstrates the utility of our approach, which is based on an analysis of the corresponding linear system on a degeneration of the plane itself, leading to a simple recursion for these dimensions. We also obtain results in the ``quasi-homogeneous'' case when all the multiplicities are equal except one; this is the natural family to consider in the recursion. | |
| dc.description | material is streamlined and some is moved to a forthcoming paper | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9702015 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9702015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148412 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Degenerations of Planar Linear Systems | |
| dc.type | text |