Effective resolution of cusps on Hilbert modular varieties. (English) Zbl 0593.14009
The author uses Shintani decomposition to give an effective construction of Ehler’s basic fan, the toroidal variety of this fan is the resolution of cusps of Hilbert modular variety.
Reviewer: K.Lai
MSC:
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
| 14J25 | Special surfaces |
References:
| [1] | DOI: 10.2748/tmj/1178228955 · Zbl 0585.14004 · doi:10.2748/tmj/1178228955 |
| [2] | DOI: 10.1007/BF01359864 · Zbl 0403.14005 · doi:10.1007/BF01359864 |
| [3] | Shintani, Automorphic Forms, Representation Theory and Arithmetic: Papers Presented at the Bombay Colloquium 1979 pp 255– (1981) |
| [4] | DOI: 10.1070/RM1978v033n02ABEH002305 · Zbl 0425.14013 · doi:10.1070/RM1978v033n02ABEH002305 |
| [5] | Hirzebruch, Lectures on Hilbert Modular Surfaces (1981) |
| [6] | DOI: 10.1007/BF01370816 · Zbl 0301.14003 · doi:10.1007/BF01370816 |
| [7] | Shintani, J. Fac. Sci. Univ 23 pp 393– (1976) |
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