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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
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