Download e-book for kindle: Algebraic Threefolds: With Special Regard to Problems of by Leonard Roth

By Leonard Roth

ISBN-10: 3540018891

ISBN-13: 9783540018896

ISBN-10: 3642855318

ISBN-13: 9783642855313

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Extra info for Algebraic Threefolds: With Special Regard to Problems of Rationality

Sample text

Let

We shall show, however, in § 3 that the surface is unirational in K(P) and representable on an involution 16 , III. n = 4: from a point P of itself the surface projects into a cubic surface, on which we are given a line p, image of P; hence, by § 3, the DEL PEZZO quartic surface is representable in K(P) on an involution 1 2 , IV. n = 5: the DEL PEZZO quintic possesses a single apparent triple point, which means that we can determine, in K, a pair of points P, Q of the surface. Projecting the surface, in its normal space 55' from P, Q, we obtain a cubic surface on which we are given a pair of skew lines p, q, images of P, Q; and this surface may be mapped birationally on a plane by drawing transversals to p and q.

1 on a curve