Higher-dimensional Analogues of Stable Curves

@inproceedings{Mori2006HigherdimensionalAO,
  title={Higher-dimensional Analogues of Stable Curves},
  author={Shingo Mori},
  year={2006}
}
The Minimal Model Program offers natural higher-dimensional analogues of stable n-pointed curves and maps: stable pairs consisting of a projective variety X of dimension ≥ 2 and a divisor B, that should satisfy a few simple conditions, and stable maps f : (X, B) → Y . Although MMP remains conjectural in higher dimensions, in several important situations the moduli spaces of stable pairs, generalizing those of Deligne-Mumford, Knudsen and Kontsevich, can be constructed more directly, and in… CONTINUE READING

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