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Surfaces of order 1 in Grassmannians. (English) Zbl 0601.14042

Let \(G\) be the Grassmannian of \(r\)-spaces in \(\mathbb P^n\), \(1\le r\le n-2\). The author presents a new proof of the Kummer classification of surfaces in \(G\) of order 1 based mainly on Bertini’s theorem. Kummer’s original proof seems not to be rigorous enough.
Reviewer: Tadeusz Józefiak

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14J10 Families, moduli, classification: algebraic theory
14N05 Projective techniques in algebraic geometry
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