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math.AG2005★ 26 cited
Resolutions of ideals of six fat points in P^2
E. Guardo, B. Harbourne
The graded Betti numbers of the minimal free resolution (and also therefore the Hilbert function) of the ideal of a fat point subscheme Z of P^2 are determined whenever Z is suppor…
math.AG2005
The (unexpected) importance of knowing
Brian Harbourne
In order to determine the Hilbert function of the ideal of a fat point subscheme of projective space, we show that it is enough to determine, both for the subscheme itself and the…
math.AG2005
Resolutions of ideals of fat points with support in a hyperplane
Giuliana Fatabbi, Brian Harbourne, Anna Lorenzini
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 multip…