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Thomas, Emery

Defects of cusp singularities. (English) Zbl 0504.14002

Math. Ann. 264, 397-411 (1983).
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MSC:

14B05 Singularities in algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14J17 Singularities of surfaces or higher-dimensional varieties
11R16 Cubic and quartic extensions
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
14J30 \(3\)-folds

Keywords:

rationality of defects series of isolated singularity; cusp singularities; Galois cubic number fields; Hilbert modular threefolds; plurigenera
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\textit{E. Thomas}, Math. Ann. 264, 397--411 (1983; Zbl 0504.14002)
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References:

[1] Cohen, H.: Variations sur un th?me de Siegel et Hecke. Acta Arith.30, 63-93 (1976) · Zbl 0291.10021
[2] Ehlers, F.: Eine Klasse komplexer Mannigfaltigkeiten und die Aufl?sung einiger isolierter Singularit?ten. Math. Ann.218, 127-156 (1975) · doi:10.1007/BF01370816
[3] Ehrhart, E.: Polyn?mes arithm?tique et m?thode des poly?dres en combinatoire. In: Int. Series of Numerical Math., Vol. 35. Basel: Birkh?user 1977
[4] Hirzebruch, F.: Hilbert modular surfaces. Enseignement Math.19, 183-281 (1974) · Zbl 0285.14007
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[8] Stanley, R.: Decompositions of rational convex polytopes. Ann. Disc. Math.6, 333-342 (1980) · Zbl 0812.52012 · doi:10.1016/S0167-5060(08)70717-9
[9] Thomas, E., Vasquez, A.: On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields. Math. Ann.247, 1-20 (1980) · doi:10.1007/BF01359864
[10] Thomas, E., Vasquez, A.: Rings of Hilbert modular forms. Composito Math.48, 139-165 (1983) · Zbl 0515.10027
[11] Weisser, D.: The arithmetic genus of the Hilbert modular variety and the elliptic fixed points of the Hilbert modular group. Math. Ann.257, 9-22 (1981) · Zbl 0467.10021 · doi:10.1007/BF01450651
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