CONTENTS
1. Introduction 1
2. Graphs 4
2.1. The graph 5
2.2. Kahler toric varieties 7
2.3. Push-forward measures 9
3. Metrics 13
3.1. Gradient spheres 13
3.2. Dependence on the metric 15
4. Uniqueness: Graph determines space 17
4.1. Building an equivariant diffeomorphism that respects the
moment maps 18
4.2. Building an isomorphism 25
5. Isolated fixed points implies toric variety 28
6. Blowing-up 38
6.1. Equivariant symplectic blow-ups and blow-downs 39
6.2. Blowing down to a minimal space 42
6.3. Minimal spaces 46
7. Completing the classification; our spaces are Kahler. 51
7.1. Algorithm 56
Appendix A. Local normal forms 57
Appendix B. Diffeomorphisms of the two-sphere 62
Appendix C. Computing a Kahler cone 63
References 69
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