22 citations · 53 across the 10 of their papers we have counts for
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math.AG2008★ 3 cited
Linear systems in P^3 with low degrees and low multiplicities
Marcin Dumnicki
We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the ca…
math.AG2008★ 4 cited
Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10
Marcin Dumnicki
In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on for , 8, 9, 10, i.e. systems of curves of given degree passing thr…
math.AG2008★ 11 cited
Regularity and non-emptyness of linear systems in
Marcin Dumnicki
The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in…