Cusps of Hilbert modular varieties

• Autores: D. B. McReynolds
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 144, Nº 3, 2008, págs. 749-759
• Idioma: inglés
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• Resumen

  • Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeo morphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingular Hilbert modular surface.