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On first order congruences of lines of \(\mathbb P^4\) with a fundamental curve. (English) Zbl 1066.14062

Manuscr. Math. 106, No. 1, 101-116 (2001); erratum ibid. 127, No. 1, 137 (2008).
Summary: We discuss projective families of lines of \(\mathbb P^n\), and in particular congruences of order one. After giving general results, we obtain a complete classification of the case of \(\mathbb P^4\) in which there is a fundamental curve.

MSC:

14N05 Projective techniques in algebraic geometry
14J40 \(n\)-folds (\(n>4\))
14M15 Grassmannians, Schubert varieties, flag manifolds
51N35 Questions of classical algebraic geometry
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