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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Characterizations of normal quintic $ K$-$ 3$ surfaces


Author: Jin Gen Yang
Journal: Trans. Amer. Math. Soc. 313 (1989), 737-751
MSC: Primary 14J28; Secondary 14J17
DOI: https://doi.org/10.1090/S0002-9947-1989-0997678-0
Erratum: Trans. Amer. Math. Soc. 330 (1992), null.
MathSciNet review: 997678
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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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DOI: https://doi.org/10.1090/S0002-9947-1989-0997678-0
Article copyright: © Copyright 1989 American Mathematical Society