Geometriae Dedicata

, Volume 139, Issue 1, pp 299–312 | Cite as

Infinitesimal variations of Hodge structure at infinity

Original Paper


By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure at finite points. As an illustration of the rich information encoded in this new structure, some instances of the maximal dimension problem for this type of infinitesimal variation are presented and contrasted with the “classical” case of IVHS at finite points.


Hodge theory Degenerating variations of Hodge structure Infinitesimal variation of Hodge structure 

Mathematics Subject Classification (2000)

14D07 32G20 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Instituto BalseiroUniversidad Nacional de Cuyo–C.N.E.A.BarilocheRepública Argentina
  2. 2.Department of MathematicsUniversity of MassachusettsAmherstUSA

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