Journal of Mathematics of Kyoto University

Twistor lines on Nagata threefold

Nobuhiro Honda

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We give an explicit description of rational curves in the product of three copies of complex projective lines, which are transformed into twistor lines in M. Nagata’s example of non-projective complete algebraic variety, viewed as the twistor space of Eguchi-Hanson metric. In particular, we show that there exist two families of such curves and both of them are parameterized by mutually diffeomorphic, connected real 4-dimensional manifolds. We also give a relationship between these two families through a birational transformation naturally associated to the Nagata’s example.

Article information

J. Math. Kyoto Univ., Volume 47, Number 4 (2007), 837-848.

First available in Project Euclid: 19 August 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J30: $3$-folds [See also 32Q25]


Honda, Nobuhiro. Twistor lines on Nagata threefold. J. Math. Kyoto Univ. 47 (2007), no. 4, 837--848. doi:10.1215/kjm/1250692292.

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