Nodal curves and postulation of generic fat points on surfaces

Details Nodal curves and postulation of generic fat points on surfaces Nodal curves and postulation of generic fat points on surfaces

1998-04-15

arxiv.org/abs/math/9804073v1

Mathematics

Algebraic Geometry

AMSTeX with AMSppt style; 5 pages

Scientific paper

Let X be a smooth projective surface. Here we study the postulation of a general union Z of fat points of X, when most of the connected components of Z have multiplicity 2. This problem is related to the existence of "good" families of curves on X, with prescribed singularities, most of them being nodes, and to the cohomology of suitable line bundles on blowing ups of X. More precise statements are obtained in the case X=P^2.

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