On the Resolution of Ideals of Fat Points

By G. Fatabbi. 2001

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A Beginner’s Guide to Edge and Cover Ideals (2013, background): “Francisco [24], Fatabbi [22] and Valla [61] have all used the splitting of monomial ideals to study the ideal of fat points in projective space P.”
On the first infinitesimal neighborhood of a linear configuration of points in P2 (2006, background): “For higher dimensional spaces we have: Catalisano, Ellia and Gimigliano [15] (arbitrary fat points whose support is on a rational normal curve in P); Fatabbi [25], Francisco [28], Fatabbi and Lorenzini [26] and Valla [56] (arbitrary fat points whose support is on ≤ n+ 1 points in P).”
Splittings of monomial ideals (2008, methodology): “Fatabbi [4], Valla [15], and the first author [5] used E-K splittings to yield results on the graded Betti numbers of some ideals of fat points.”
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers (2006, methodology): “This relation was first observed for the total Betti numbers by Eliahou and Kervaire [8] and extended to the graded case by Fatabbi [10].”