Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 47, Number 4 (2007), 837-848.
Twistor lines on Nagata threefold
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.
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. https://projecteuclid.org/euclid.kjm/1250692292