Brian Harbourne

Comparing powers and symbolic powers of ideals

We develop tools to study the problem of containment of symbolic powers

Complete linear systems on rational surfaces

I^{(m)}

Anticanonical Rational Surfaces

in powers

Free resolutions of fat point ideals onP2

I^r

Classifying Hilbert functions of fat point subschemes in ℙ2

for a homogeneous ideal

Linear subspaces, symbolic powers and Nagata type conjectures

I

The Ideal Generation Problem for Fat Points

in a polynomial ring

Negative curves on algebraic surfaces

k[{\bf P}^N]

Resolutions of ideals of quasiuniform fat point subschemes of

in

Resolutions of ideals of any six fat points in P2

N+1