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On hypersurfaces in \(\mathbb P^3\) with fat points in general position. (English) Zbl 1178.14054

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)].

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)

Citations:

Zbl 1170.14039
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