Variations of Hodge structure, expressed by meromorphic differentials on the projective plane

TitleVariations of Hodge structure, expressed by meromorphic differentials on the projective plane
Publication TypeJournal Article
Year of Publication2000
AuthorsKasparian A
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume92
IssueLivre 1 - Mathématiques et Mecanique
Pagination17-30
ISSN0205-0808
Keywordsabelian-motivic and hypersurface variations, tautological variations of Hodge structure and $J$ - Hodge structure
Abstract

The tautological variations of Hodge structure over Siegel upper half space, the open quadric and the generalized ball are expressed explicitely by the variations of Hodge structure of Weil hypersurfaces in projective spaces. That realizes all the abelian-motivic variations of Hodge structure by families of Jacobians of plane curves, which are known to be described by meromorphic differentials on the projective plane. As a consequence, the geometric origin of a maximal dimensional variation of Hodge structure turns to be sufficient for expressing it by meromorphic differentials on the projective plane.

1991/95 MSC

14D07, 14K10

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