10 papers
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…
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…
Hilbert functions and resolutions for ideals of n = s^2 fat points in P2
Brian Harbourne, Joaquim Roé
Conjectures for the Hilbert function of the m-th symbolic power of the ideal of n general points of P2 are verified for infinitely many m for each square n > 9, using an approach d…
Seshadri constants and very ample divisors on algebraic surfaces
Brian Harbourne
A broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given; it works for all surfaces in all characteristi…
Problems and progress: survey on fat points in P2
Brian Harbourne
This paper surveys certain problems involving numerical characters for ideals I(Z) defining fat points subschemes for general points . It al…
Resolutions of fat point ideals involving 8 general points of P2
Stephanie Fitchett, Brian Harbourne, Sandeep Holay
The main result provides an algorithm for determining the minimal free resolution of ideals of fat point subschemes of involving up to 8 general points with arbitrary m…