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October 2016 Pseudonorms and theorems of Torelli type
Chen-Yu Chi
J. Differential Geom. 104(2): 239-273 (October 2016). DOI: 10.4310/jdg/1476367057


We show that for every positive integer n, there exists an explicit positive integer cn that only depends on n such that if $M$ and $M^{\prime}$ are canonically polarized complex projective manifolds of dimension $n$ and if $H^0 (M, mK_M)$ and $H^0(M^{\prime}, mK_{M^{\prime}})$ are linearly isometric with respect to the pseudonorm $\langle\!\langle\ \rangle\!\rangle$ for some $m \geqslant c_n$, then $M$ and $M^{\prime}$ 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.


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Chen-Yu Chi. "Pseudonorms and theorems of Torelli type." J. Differential Geom. 104 (2) 239 - 273, October 2016.


Published: October 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1355.14008
MathSciNet: MR3557304
Digital Object Identifier: 10.4310/jdg/1476367057

Rights: Copyright © 2016 Lehigh University


Vol.104 • No. 2 • October 2016
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