Geodesic
Hilbert--Kuga--Sato varieties and parabolic differentials
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 94-113

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The behavior of parabolic forms relative to the Hilbert modular group and certain transcendental cycles is studied on Hilbert and Kuga–Sato varieties in a neighborhood of the divisors of a smooth compactification. 
@article{ZNSL_1979_86_a9,
     author = {M. I. Kifer and I. A. Skornyakov},
     title = {Hilbert--Kuga--Sato varieties and parabolic differentials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--113},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a9/}
}
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M. I. Kifer; I. A. Skornyakov. Hilbert--Kuga--Sato varieties and parabolic differentials. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 94-113. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a9/