In 1970, Phillip Griffiths estimated that issues at infinity can be additional to the classifying house D of polarized Hodge constructions. during this ebook, Kazuya Kato and Sampei Usui notice this dream through making a logarithmic Hodge thought. They use the logarithmic buildings started via Fontaine-Illusie to restore nilpotent orbits as a logarithmic Hodge structure.
The e-book specializes in relevant themes. First, Kato and Usui build the advantageous moduli area of polarized logarithmic Hodge constructions with extra buildings. Even for a Hermitian symmetric area D, the current conception is a refinement of the toroidal compactifications by way of Mumford et al. For basic D, advantageous moduli areas could have slits because of Griffiths transversality on the boundary and be not in the community compact. moment, Kato and Usui build 8 enlargements of D and describe their kin via a basic diagram, the place 4 of those enlargements stay within the Hodge theoretic region and the opposite 4 dwell within the algebra-group theoretic quarter. those components are attached via a continuing map given through the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the development within the first topic.
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