张祺教授
报告
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的摘要
张祺教授报告的摘要:
A variety $X$ is said to be uniruled (resp : rationally connected) if for any point $x$ (resp : a pair of points $x$ and $y$) in $X$, there exists a rational curve which contains $x$ (resp : $x$ and $y$).
Q-Fano varieties are those which are similar to del Pezzo surfaces (but higher dimensional with certain singularities). Q-Fano varieties play an increasingly important role in Mori's program. They are known to be uniruled (by the work of Miyaoka-Mori). A famous conjecture of Kollar-Miyaoka-Mori predicts that they should be rationally connected.
In this talk I shall explore the history and some ramifications of the conjecture. I shall also explain the work in which I was able to give an affirmative answer to the conjecture as well as some applications to the study of projective varieties with nef anti-canonical divisor.