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On quintic surfaces of general type. (English) Zbl 0596.14029

The minimal model \(\tilde S\) of an irreducible quintic surface \(S\subset {\mathbb{P}}^ 3({\mathbb{C}})\) is of general type if S is normal and has at most rational double points (called non essential singularities). The author shows that the condition ”\(\tilde S\) of general type” implies that S is normal and has at most elliptic double or triple points as essential singularities. The known classification of those singularities allows a classification of the quintic surfaces of general type. In addition the author is able to describe in some cases the corresponding Hilbert scheme.
Reviewer: E.Viehweg

MSC:

14J25 Special surfaces
14J10 Families, moduli, classification: algebraic theory
14B05 Singularities in algebraic geometry
14E30 Minimal model program (Mori theory, extremal rays)
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