Linear systems with multiple base points in P2

Details Linear systems with multiple base points in P2 Linear systems with multiple base points in P2

2001-01-12

arxiv.org/abs/math/0101109v2

Mathematics

Algebraic Geometry

Final version, to appear in Advances in Geometry. Largely rewritten, now includes results determining Hilbert functions (resol

Scientific paper

Given positive integers $m_1, m_2, ..., m_n$, and $n$ general points $p_i$ of ${\bf CP}^2$, bounds are given for the least degree $t$ among plane curves passing through each point $p_i$ with multiplicity at least $m_i$, and for the least $t$ such that the $n$ multiple points impose independent conditions on curves of degree $t$, often improving substantially what was previously known. As an application, the Hilbert function (resp., minimal free resolution) is determined for symbolic powers $I^{(m)}$ for the ideal $I$ defining $n$ general points of ${\bf CP}^2$ for infinitely many m for each square n (resp., for infinitely many m for each even square n). Four graphs are included showing other values of m and n for which results are given.

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