×

Simultaneous resolution of rational singularities. (English) Zbl 0412.14008


MSC:

14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14J15 Moduli, classification: analytic theory; relations with modular forms
14G05 Rational points
32S45 Modifications; resolution of singularities (complex-analytic aspects)
32S30 Deformations of complex singularities; vanishing cycles
14D20 Algebraic moduli problems, moduli of vector bundles

Citations:

Zbl 0405.14010
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[1] V.I. Arnold : On matrices depending on parameters . Russian Math Surveys 26 #2 (1971) 29-43. · Zbl 0259.15011
[2] M. Artin : Algebraic construction of Brieskorn’s resolutions . Journal of Algebra 29 (1974) 330-348. · Zbl 0292.14013
[3] M. Artin : On isolated rational singularities of surfaces . Amer. J. Math. 88 (1966) 129-137. · Zbl 0142.18602
[4] M. Atiyah : On analytic surfaces with double points . Proc. Roy. Soc. A 247 (1958) 237-244. · Zbl 0135.21301
[5] E. Brieskorn : Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen . Math. Ann. 166 (1966) 76-102. · Zbl 0145.09402
[6] E. Brieskorn : Die Auflösung der rationalen Singularitäten holomorpher Abbildungen . Math. Ann. 178 (1968) 255-270. · Zbl 0159.37703
[7] E. Brieskorn : Singular elements of semi-simple algebraic groups . Actes. Congrès Inter. Math. 2 (1970) 279-284. · Zbl 0223.22012
[8] D. Burns and M. Rapoport : On the Torelli problem for Kählerian K-3 surfaces . Ann. Sci. École Norm. Sup. 8 (1975) 235-274. · Zbl 0324.14008
[9] D. Burns and J. Wahl : Local contributions to global deformations of surfaces . Inv. Math. 26 (1974) 67-88. · Zbl 0288.14010
[10] A. Fujuki and S. Nakano : Supplement to On the inverse of monoidal transformation . Publ. Res. Inst. Math. Sci. Kyoto Univ. 7 (1971-72) 637-644. · Zbl 0234.32019
[11] E. Horikawa : Algebraic surfaces of general type with small c21, II . Inv. Math. 37 (1976) 121-155. · Zbl 0339.14025
[12] F. Huikeshoven : On the versal resolutions of deformations of rational double points . Inv. Math. 20 (1973) 15-34. · Zbl 0268.32010
[13] A. Kas : On the resolutions of certain holomorphic mappings . Global Analysis , Tokyo (1969). · Zbl 0192.57902
[14] J. Lipman : Rational singularities with applications to algebraic surfaces and unique factorization . Publ. Math. I.H.E.S. 36 (1969) 195-279. · Zbl 0181.48903
[15] J. Lipman : Double point resolutions of deformations of rational singularities . Comp. Math. 38 (1979) 37-42. · Zbl 0405.14010
[16] H. Pinkham : Deformations of cones with negative grading . Jour. of Alg. 30 (1974) 92-102. · Zbl 0284.14009
[17] O. Riemenschneider : Deformations of rational singularities and their resolutions . Rice Univ. Stud. 59 (1973) 119-130. · Zbl 0278.32010
[18] G.N. Tjurina : Absolute isolatedness of rational singularities and triple rational points . Funct. Anal. App. 2 (1968) 324-332. · Zbl 0176.50804
[19] G.N. Tjurina : Resolution of singularities of plane deformations of double rational points . Funct. Anal. App. 4 (1970) 68-73. · Zbl 0221.32008
[20] J. Wahl : Vanishing theorems for resolutions of surface singularities . Inv. Math. 31 (1975) 17-41. · Zbl 0314.14010
[21] J. Wahl : Local cohomology groups for resolutions of singularities . Symposia in Pure Math. 30 (1977) 91-94. · Zbl 0371.14004
[22] J. Wahl : Equisingular deformations of normal surface singularities , I. Ann. of Math. 104 (1976) 325-356. · Zbl 0358.14007
[23] J. Wahl : Equations defining rational singularities . Ann. Sci. École Norm. Sup. 10 (1977) 231-264. · Zbl 0367.14004
[24] J. Wahl : On Res \rightarrow Def for a rational singularity . Informal Research Announcement (1976).
[25] J. Wahl : Simultaneous resolution and discriminantal loci . (to appear). · Zbl 0472.14002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.