Journal of Mathematics of Kyoto University

Twistor lines on Nagata threefold

Nobuhiro Honda

Full-text: Open access


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

Permanent link to this document

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.

Export citation