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A bound of the degree of some rational surfaces in $${\mathbb P}^4$$. (English) Zbl 1035.14013
Summary: In this paper we find a bound of the degree of rational surfaces embedded in $${\mathbb P}^4$$ with linear systems of type $| {\mathcal L} -px_0-x_1-\dots-x_r|,\quad p\geq 2,\;{\mathcal L}\text{ ample linear system}.$ We determine all the possible (families of) rational surfaces embedded in $${\mathbb P}^4$$ with linear systems as above, for the particular case $$p=2$$.
##### MSC:
 14J26 Rational and ruled surfaces 14N05 Projective techniques in algebraic geometry 14C20 Divisors, linear systems, invertible sheaves
##### Keywords:
rational surface; projective space; linear systems
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