The intersection cohomology of the Satake compactification of Ag for g≤4

We completely determine the intersection cohomology of the Satake compactifications A 2 Sat , A 3 Sat , and A 4 Sat , except for I H 10 ( A 4 Sat ) . We also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the Satake compact...

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Bibliographic Details
Published in:Mathematische annalen 2017-12, Vol.369 (3-4), p.1353-1381
Main Authors: Grushevsky, Samuel, Hulek, Klaus
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:We completely determine the intersection cohomology of the Satake compactifications A 2 Sat , A 3 Sat , and A 4 Sat , except for I H 10 ( A 4 Sat ) . We also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the Satake compactification in these genera. As a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-016-1491-1