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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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