An Algorithm for Fat Points on P2
| dc.creator | Harbourne, Brian | |
| dc.date | 1998-03-26 | |
| dc.date | 1999-09-16 | |
| dc.date.accessioned | 2026-07-07T05:24:13Z | |
| dc.date.available | 2026-07-07T05:24:13Z | |
| dc.description | Let $F$ be a line bundle on the blow-up $X$ of $P^2$ at $r$ general points $p_1, ..., p_r$ and let $L$ be the pullback to $X$ of the line bundle coming from a line on $P^2$. Under reasonable hypotheses that are conjectured always to hold if the points $p_1, ..., p_r$ are sufficiently general, it is shown that the computation of the dimension of the cokernel of the natural map $μ_F:Γ(F)\otimesΓ(L)\toΓ(F\otimes L)$ reduces to the case that $F$ is ample. As an application, a complete determination of the dimension of the cokernel of $μ_F$ is obtained when $r\le 7$, thereby solving the Ideal Generation Problem for fat point subschemes involving up to 7 general points of the plane and giving an algorithm depending only on the multiplicities $m_i$ for determining the modules in a minimal free resolution of the ideal defining a fat point subscheme $m_1p_1+...+ m_7p_7$ for general points $p_i$. All results hold for an arbitrary algebraically closed ground field $k$. | |
| dc.description | 14 pages; plaintex; improved exposition in introduction; for an on-line implementation of the algorithm, go to http://www.math.unl.edu/~bharbour/cgi-bin/7fatpts.cgi | |
| dc.identifier | https://arxiv.org/abs/math/9803131 | |
| dc.identifier | http://arxiv.org/abs/math/9803131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76750 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14C99, 13P10 (primary); 13D02, 13H15 (secondary) | |
| dc.title | An Algorithm for Fat Points on P2 | |
| dc.type | text |