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Double structures on Bordiga surfaces. (English) Zbl 0706.14025
A Bordiga surface S is a projective plane birationally embedded into \(P^ 4\) by quartics through given 10 points, so that its degree equals 6. The present paper studies when such surface is a set-theoretical complete intersection of a cubic and a quartic. This relates to the existence of a double structure on S, and the latter may relate to a vector bundle of rank 2 on \(P^ 4\) (which splits in the present case). The author proves that such a double structure exists if and only if S contains a certain curve C of degree 4 and is contained in the secant variety of C. Here C is either a normal rational curve or a union of two conics which intersect at one point. The 10 points on \(P^ 2\) to be blown up are also determined in these cases.
Reviewer: E.Horikawa

14J26 Rational and ruled surfaces
14M10 Complete intersections
Full Text: DOI
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