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) |
Keywords:
triple points; minimal model; double points; classification of the quintic surfaces of general type; Hilbert schemeReferences:
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