On a construction of the twistor spaces of Joyce metrics, I

Details On a construction of the twistor spaces of Joyce metrics, I On a construction of the twistor spaces of Joyce metrics, I

2006-03-10

arxiv.org/abs/math/0603242v2

Mathematics

Differential Geometry

22 pages, 9 figures; V2: errors and typos corrected, presentation improved

Scientific paper

In 1995 D. Joyce explicitly constructed a series of self-dual metrics with torus action on the connected sums of complex projective planes. In this paper we explicitly construct the twistor spaces of some of Joyce's self-dual metrics. Starting from a fiber space whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the required twistor spaces. In the construction an important role is played by flops, a useful operation in algebraic geometry.

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