Let F: V→ B be a smooth non-isotrivial 1 - dimensional family of complex polarized abelian varieties and Vb= F- 1(b) be the general fiber. Let F1⊂ R1F∗C be the associated Hodge bundle filtration, Fb1=H1.0(Vb). Under the assumption that the Fujita decomposition for F1 is non trivial, that is there is a non trivial flat sub-bundle 0 ≠ U⊂ F1, we show that Vb has non-trivial endomorphism: End(Vb) ≠ Z.
Fujita decomposition on families of abelian varieties
Pirola G. P.
2021-01-01
Abstract
Let F: V→ B be a smooth non-isotrivial 1 - dimensional family of complex polarized abelian varieties and Vb= F- 1(b) be the general fiber. Let F1⊂ R1F∗C be the associated Hodge bundle filtration, Fb1=H1.0(Vb). Under the assumption that the Fujita decomposition for F1 is non trivial, that is there is a non trivial flat sub-bundle 0 ≠ U⊂ F1, we show that Vb has non-trivial endomorphism: End(Vb) ≠ Z.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
