A fibre criterion for a polynomial to belong to an ideal.
On hypersurfaces in with fat points in general position.
Cutting diagram method for systems of plane curves with base points
We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.
Quasi-homogeneous linear systems on ℙ² with base points of multiplicity 7, 8, 9, 10
We prove that the Segre-Gimigliano-Harbourne-Hirschowitz conjecture holds for quasi-homogeneous linear systems on ℙ² for m = 7, 8, 9, 10, i.e. systems of curves of a given degree passing through points in general position with multiplicities at least m,...,m,m₀, where m = 7, 8, 9, 10, m₀ is arbitrary.
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