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- W2008103631 abstract "Arakelov–Parshin rigidity is concerned with varieties mapping rigidly to the moduli stack $$mathfrak {M}_h$$ of canonically polarized manifolds. Affirmative answer for any class of maps implies finiteness of the given class. This article studies Arakelov–Parshin rigidity on an open subspace of $$mathfrak {M}_h$$ , on the locus $$mathfrak {K}mathfrak {F}_h$$ of iterated Kodaira fibrations. First, we prove rigidity for all complete curves mapping finitely onto $$mathfrak {K}mathfrak {F}_h$$ . Then, for generic affine curves mapping into $$mathfrak {K}mathfrak {F}_h$$ , rigidity is shown when $$deg h =2$$ . The method used in the latter part is showing that the iterated Kodaira–Spencer map is injective." @default.
- W2008103631 created "2016-06-24" @default.
- W2008103631 creator A5021889008 @default.
- W2008103631 date "2014-07-26" @default.
- W2008103631 modified "2023-09-27" @default.
- W2008103631 title "Arakelov–Parshin rigidity of towers of curve fibrations" @default.
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- W2008103631 doi "https://doi.org/10.1007/s00209-014-1336-0" @default.
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