Mathematics – Algebraic Geometry
Scientific paper
2005-02-19
Mathematics
Algebraic Geometry
10 pages; to appear in Proc. Amer. Math. Soc.; some expositional changes; added a reference to paper of Geramita, Migliore and
Scientific paper
Our results concern minimal graded free resolutions of fat point ideals for points in a hyperplane. Suppose, for example, that I(m,d) is the ideal defining r given points of multiplicity m in the projective space P^d. Assume that the given points lie in a hyperplane P^{d-1} in P^d, and that the ground field k is algebraically closed of characteristic 0. We give an explicit minimal graded free resolution of I(m,d) in k[P^d] in terms of the minimal graded free resolutions of the ideals I(j,d-1) in k[P^{d-1}] with j < m+1. As a corollary, we give the following formula for the Poincare polynomial P_{m,d} of I(m,d) in terms of the Poincare polynomials P_{j,d-1} of I(j,d-1): P_{m,d} = (1 + XT)(\Sigma_{0
Fatabbi Giuliana
Harbourne Brian
Lorenzini Anna
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