## Journal of Mathematics of Kyoto University

### Twistor lines on Nagata threefold

Nobuhiro Honda

#### Abstract

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

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

Dates
First available in Project Euclid: 19 August 2009

https://projecteuclid.org/euclid.kjm/1250692292

Digital Object Identifier
doi:10.1215/kjm/1250692292

Mathematical Reviews number (MathSciNet)
MR2413068

Zentralblatt MATH identifier
1167.32014

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

#### Citation

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