Dumnicki, Marcin On hypersurfaces in \(\mathbb P^3\) with fat points in general position. (English) Zbl 1178.14054 Zesz. Nauk. Uniw. Jagiell. 1303, Univ. Iagell. Acta Math. 46, 15-19 (2008). Summary: We prove that a linear system of hypersurfaces in \(\mathbb P^3\) of degree \(d\), \(14\leq d\leq 40\), with double, triple and quadruple points in general position is non-special. This solves the cases that have not been completed in a paper by E. Ballico and M. C. Brambilla [J. Pure Appl. Algebra 213, No. 6, 1002–1012 (2009; Zbl 1170.14039)]. Cited in 3 Documents MSC: 14N05 Projective techniques in algebraic geometry 14C20 Divisors, linear systems, invertible sheaves 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Keywords:linear systems; fat points Citations:Zbl 1170.14039 PDFBibTeX XMLCite \textit{M. Dumnicki}, Zesz. Nauk. Uniw. Jagiell., Univ. Iagell. Acta Math. 1303(46), 15--19 (2008; Zbl 1178.14054) Full Text: EuDML