## 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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### References:

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