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On Veronesean surfaces. (English) Zbl 0701.14014
The subject of this paper is the study of rational projective surfaces which arise as embeddings of blowing-ups of $${\mathbb{P}}^ 2$$ at a set of distinct points $$P_ 1,...,P_ s$$, via linear systems of curves of degree $$d$$ with $$s\leq {d+1\choose 2}$$ passing through the $$P_ i's.$$
A preliminary version of this work is published in Curves Semin. Queen’s, Vol. 4, Kingston/Ontario 1985/86, Queen’s Pap. Pure Appl. Math. 76 (1986; Zbl 0651.14022). - For further developments on this kind of problems see also A. V. Geramita and the author, “Generators for the defining ideal of certain rational surfaces”, Duke Math. J. (to appear).
Reviewer: A.Gimigliano

##### MSC:
 14E25 Embeddings in algebraic geometry 14M12 Determinantal varieties