Characterizations of normal quintic 𝐾-3 surfaces

Yang, Jin Gen

doi:10.1090/S0002-9947-1989-0997678-0

Characterizations of normal quintic $K$-$3$ surfaces
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Trans. Amer. Math. Soc. 313 (1989), 737-751 Request permission

Erratum: Trans. Amer. Math. Soc. 330 (1992), 461.

Abstract:

If a normal quintic surface is birational to a $K$-$3$ surface then it must contain from one to three triple points as its only essential singularities. A $K$-$3$ surface is the minimal model of a normal quintic surface with only one triple point if and only if it contains a nonsingular curve of genus two and a nonsingular rational curve crossing each other transversally. The minimal models of normal quintic $K$-$3$ surfaces with several triple points can also be characterized by the existence of some special divisors.

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