Twistor lines on Nagata threefold

2006/08/18 by Nobuhiro Honda, Honda, Nobuhiro
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.math/0608455

V2: 10 pages, 1 figure; a figure explaining key fact added, comments on automorphism group added. Accepted for publication in J. Math. Kyoto Univ

openalex publication_date 2006/08/18 · arxiv created 2007/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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