Pseudonorms and theorems of Torelli type
Pseudonorms and theorems of Torelli type
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DOI：
10.4310/jdg/1476367057
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发表时间：
2016-10
影响因子：
2.5
通讯作者：
Chen-Yu Chi
中科院分区：
文献类型：
--
作者：
Chen-Yu Chi
We show that for every positive integer n , there exists an ex-plicit positive integer c n that only depends on n such that if M and M (cid:2) are canonically polarized complex projective manifolds of dimension n and if H 0 ( M, mK M ) and H 0 ( M (cid:2) , mK M (cid:2) ) are linearly isometric with respect to the pseudonorm (cid:2)(cid:2) (cid:3)(cid:3) for some m (cid:2) c n , then M and M (cid:2) are isomorphic. This generalizes a result of Royden for compact Riemann surfaces of genus greater than or equal to 2. The same approach is used to prove similar and weaker results for projective manifolds with nonnegative Kodaira dimension. We also introduce a kind of singular index for singularities of pairs that refines the traditional log canonical threshold.
