Ky Fan Lecture

主講者: | Yoichi Miyaoka(The University of Tokyo) |

講題: | On the canonical degree of curves on a surface |

時間: | 2012-11-22 (Thu.) 16:15 - 17:15 |

地點: | |

Abstract: | A conjecture of Lang predicts that a variety of general type $X$ contains a proper closed algebraic subset $Z$ such that all the rational curves and elliptic curves on $X$ are necessarily contained in $Z$. Though Kodaira proved a weaker result to the effect that the union of all the rational/elliptic curves on $X$ has Lebesgue measure zero, the conjecture is still wide open, even in the case where $X$ is a surface. We discuss this problem and prove that, if $X$ satisfies a certain topological condition, we can effectively bound the number of rational/elliptic curves on $X$. |

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