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On the irreducibility of Hilbert scheme of surfaces of minimal degree. (English) Zbl 1262.14004

The Hilbert scheme of irreducible surfaces of degree \(m\) in projective \({\mathbb P}^{m+1}\) is irreducible, except for \(m=4\) when the Hilbert scheme has two components. The article provides a new proof of this result using generic coverings of the projective plane.

MSC:

14C05 Parametrization (Chow and Hilbert schemes)
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