@article{CM_1985__56_1_3_0, author = {Ebeling, W. and Wall, C. T. C.}, title = {Kodaira singularities and an extension of {Arnold's} strange duality}, journal = {Compositio Mathematica}, pages = {3--77}, publisher = {Martinus Nijhoff Publishers}, volume = {56}, number = {1}, year = {1985}, mrnumber = {806842}, zbl = {0586.14033}, language = {en}, url = {http://www.numdam.org/item/CM_1985__56_1_3_0/} }
TY - JOUR AU - Ebeling, W. AU - Wall, C. T. C. TI - Kodaira singularities and an extension of Arnold's strange duality JO - Compositio Mathematica PY - 1985 SP - 3 EP - 77 VL - 56 IS - 1 PB - Martinus Nijhoff Publishers UR - http://www.numdam.org/item/CM_1985__56_1_3_0/ LA - en ID - CM_1985__56_1_3_0 ER -
Ebeling, W.; Wall, C. T. C. Kodaira singularities and an extension of Arnold's strange duality. Compositio Mathematica, Volume 56 (1985) no. 1, pp. 3-77. http://www.numdam.org/item/CM_1985__56_1_3_0/
[1] The Lefschetz theorem on hyperplane sections. Annals of Math. 69 (1959) 713-717. | MR | Zbl
and :[2] Remarks on the stationary phase method and Coxeter numbers. Usp. Math. Nauk. 28 (1973) (5), 17-44(Engl. translation in Russ. Math. Surv. 28 (1973) 5, 19-48. | MR | Zbl
:[3] Normal forms of functions in a neighbourhood of a degenerate critical point. Usp. Math. Nauk. 29 (1974) 2, 11-49(Engl. translation in Russ. Math. Surv. 29 (1974) 2, 10-50). | MR | Zbl
:[4] Critical points of smooth functions and their normal forms. Usp. Math. Nauk. 30 (1975) 5, 3-65(Engl. translation in Russ. Math. Surv. 30 (1975) 5, 1-75). | MR | Zbl
:[5] On isolated rational singularities of surfaces. Amer. J. Math. 88 (1966) 129-136. | MR | Zbl
:[6] Die Monodromie der isolierten Singularitäten von Hyperflächen. Manuscripta math. 2 (1970) 103-160. | MR | Zbl
:[7] Die Milnorgitter der exzeptionellen unimodularen Singularitäten. Bonner Mathematische Schriften Nr. 150, Bonn (1983). | MR | Zbl
:[8] Groupes et Algèbres de Lie, Chaps. 4, 5 et 6. Paris, Hermann (1968). | MR
:[9] Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3. Amer. J. Math. 99 (1977) 447-485. | MR | Zbl
and :[10] Quotient-conical singularities on complex surfaces. Funkt. Anal. Jego Prilozh. 8 (1974) 2, 75-76(Engl. translation in Funct. Anal. Appl. 8 (1974) 160-161). | Zbl
:[11] Automorphic forms and quasihomogeneous singularities. Funkt. Anal. Jego Prilozh. 9 (1975) 2, 67-68(Engl. translation in Funct. Anal. Appl. 9 (1975) 149-151). | Zbl
:[12] On the link space of a Gorenstein quasihomogeneous surface singularity. Math. Ann. 265 (1983) 529-540. | MR | Zbl
:[13] The signature of smoothings of complex surface singularities. Math. Ann. 232 (1978) 85-98. | MR | Zbl
:[14] Fifteen characterizations of rational double points and simple critical points. l'Enseignement Math. 25 (1979) 131-163. | MR | Zbl
:[15] On the singularities which do not affect the condition of adjunction (Part I). Proc. Camb. Phil. Soc. 30 (1934) 483-491. | JFM | Zbl
:[16] Quadratische Formen und Monodromiegruppen von Singularitäten. Math. Ann. 255 (1981) 463-498. | MR | Zbl
:[17] Arithmetic monodromy groups. Math. Ann. 264 (1983) 241-255. | MR | Zbl
:[18] Milnor lattices and geometric bases of some special singularities. L'Enseignement Math. 29 (1983) 263-280. | MR | Zbl
:[19] An arithmetic characterisation of the symmetric monodromy groups of singularities. Invent. Math. 77 (1984) 85-99. | MR | Zbl
:[20a]Dynkin diagrams of unimodal singularites. Funkt. Anal. Jego Prilozh. 8 (1974) 3, 1-6(Engl. translation in Funct. Anal. Appl. 8 (1974) 192-196). | MR | Zbl
:[20b]Adjoining spectra of certain singularities. Vestnik Mos. Univ. Ser. 1, Math. Mech. 4 (1981) 19-22 (in Russian). | MR | Zbl
:[21] On the topology of smoothable singularities. Proc. of Symp. in Pure Math. Vol. 40, Part 1 (1983) 535-545. | MR | Zbl
and :[22] Lokale topologische Eigenschaften komplexer Räume. Math. Ann. 191 (1971) 235-252. | MR | Zbl
:[23] Hilbert modular surfaces. L'Enseignement Math. 19 (1973) 183-282. | MR | Zbl
:[24] Classification of Hilbert modular surfaces. In: Complex analysis and algebraic geometry (W.L. Baily and T. Shioda, eds.), Cambridge University Press (1977) pp. 43-77. | MR | Zbl
and :[25a]New surfaces with no meromorphic functions. Proc. Internat. Cong. Math. Vancouver. Vol. 1 (1974) 423-426. | MR | Zbl
:[25b] New surfaces with no meromorphic functions II. In: Complex analysis and algebraic geometry (W.L. Baily and T. Shioda, eds.), Cambridge University Press (1977) pp. 91-106. | MR | Zbl
:[26] Infinite root systems, representations of graphs and invariant theory. Invent. Math. 56 (1980) 57-92. | MR | Zbl
:[27] Klassifikation 2-dimensionaler Singularitäten mit auflösbaren lokalen Fundamentalgruppen. Math. Ann. 213 (1975) 231-255. | MR | Zbl
:[28] Eigenschaften der lokalen Ringe in zweidimensionalen Spitzen. Math. Ann. 215 (1975) 117-129. | MR | Zbl
:[29] Deformations of cusp singularities. Proc. of Symp. in Pure Math. Vol. 30 (1977) 37-44. | MR | Zbl
:[30] On pencils of curves and deformations of minimally elliptic singularities. Math. Ann. 247 (1980) 43-65. | MR | Zbl
:[31] On compact analytic surfaces II. Ann. of Math. 77 (1963) 563-626. | Zbl
:[32] Degenerate elliptic curves and resolution of uni- and bimodal singularities. Funkt. Anal. Jego Prilozh. 9 (1975) 1, 72-73; (Engl. translation in Funct. Anal. Appl. 9 (1975) 69-70. | MR | Zbl
:[33] Taut 2-dimensional singularities. Math. Ann. 205 (1973) 131-164. | MR | Zbl
:[34] On μ for surface singularities. Proc. of Symp. in Pure Math. Vol. 30 (1977) 45-49. | Zbl
:[35] On minimally elliptic singularities. Amer. J. Math. 99 (1977) 1257-1295. | MR | Zbl
:[36] Ambient deformations for exceptional sets in two-manifolds. Invent. Math. 55 (1979) 1-36. | MR | Zbl
:[37] Rational surfaces with an anti-canonical cycle. Annals of Math. 114 (1981) 267-322. | MR | Zbl
:[38] The smoothing components of a triangle singularity I. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 173-183. | MR | Zbl
:[39] Quadratic functions and smoothing surface singularities. Topology (to appear). | MR | Zbl
and :[40] Stability of C∞-mappings III: Finitely determined map germs. Publ. Math. I.H.E.S. 35 (1968) 127-156. | Numdam | Zbl
:[41] Singular points of complex hypersurfaces. Ann. of Math. Studies, Princeton (1968). | MR | Zbl
:[42] On the 3-dimensional Brieskorn manifolds M( p, q, r). In: Knots, groups and 3-manifolds. Papers dedicated to the memory of R.H. Fox (L.P. Neuwirth ed.), Ann. of Math. Studies, Princeton University Press (1975) pp. 175-225. | MR | Zbl
:[43] The transversality characteristic class and linking cycles in surgery theory. Annals of Math. 99 (1974) 463-544. | MR | Zbl
and :[44] Inoue-Hirzebruch surfaces and a duality of hyperbolic unimodular singularities I. Math. Ann. 252 (1980) 221-235. | MR | Zbl
:[45] Duality of cusp singularities. In: Complex analysis of singularities (R.I.M.S. Symposium, K. Aomoto, organizer), Kyoto (1981) pp. 1-18.
:[46] Geometry of quasihomogeneous surface singularities. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 245-258. | MR | Zbl
:[47] Integral symmetric bilinear forms and some of their applications. Izv. Akad. Nauk. SSSR Ser. Mat. 43 (1979) 111-177(Engl. translation in Math. USSR Izv. 14, No. 1 (1980) 103-167). | MR | Zbl
:[48] Deformations of algebraic varieties with G m action. Astérisque 20, Soc. Math. de France (1974). | Numdam | MR | Zbl
:[49] Singularités exceptionelles, la dualité étrange d'Arnold et les surfaces K-3. C.R. Acad. Sc. Paris, Série A, 284 (1977) 615-618. | MR | Zbl
:[50] Groupe de monodromie des singularités unimodulaires exceptionelles. C.R. Acad. Sc. Paris, Série A, 284 (1977) 1515-1518. | MR | Zbl
:[51] Smoothings of the Dpqr singularities, p + q + r = 22. Appendix to Looijenga's paper: The smoothing components of a triangle singularity. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 373-377. | MR | Zbl
:[52] Automorphisms of cusps and Inoue-Hirzebruch surfaces. Compositio Math. 52 (1984) 299-313. | Numdam | MR | Zbl
:[53] Elliptic Gorenstein singularities. Unpublished manuscript (1973).
:[54] Einfach-elliptische Singularitäten. Invent. Math. 23 (1974) 289-325. | MR | Zbl
:[55] The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983) 401-487. | MR | Zbl
:[56] A cobordism invariant for surface singularities. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 479-484. | MR | Zbl
:[57] Intersection form for quasi-homogeneous singularities. Compositio Math. 34 (1977) 211-223. | Numdam | MR | Zbl
:[58] Mixed Hodge structure on the vanishing cohomology. In: Real and complex singularities (P. Holm ed.), Sijthoff & Noordhoff (1977) pp. 525-563. | MR | Zbl
:[59] Mixed Hodge structures associated with isolated singularities. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 513-536. | MR | Zbl
:[60] The geometry and topology of 3-manifolds. Notes. Princeton (1978-79).
:[61] Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. AMS 6 (1982) 357-382. | MR | Zbl
:[62] An invariant of quadratic forms mod. 8. Kon. Ned. Akad. van Wet. (A) 62 (1959) 291-293. | MR | Zbl
:[63] Smoothings of normal surface singularities. Topology 20 (1981) 219-246. | MR | Zbl
:[64] Deformation von Gorenstein-Singularitäten der Kodimension 3. Math. Ann. 242 (1979) 201-208. | MR | Zbl
:[65] Classification problems in differential topology-VI: Classification of (s-1)-connected (2s + 1)-manifolds. Topology 6 (1967) 273-296. | MR | Zbl
:[66] Classification of unimodal isolated singularities of complete intersections. Proc. of Symp. in Pure Math. Vol. 40, Part 2 (1983) 625-640. | MR | Zbl
:[67] Notes on the classification of singularities. Proc. Lond. Math. Soc. 48 (1984) 461-513. | MR | Zbl
:[68] Certain invariant subrings are Gorenstein, I, II. Osaka J. Math. 11 (1974) 1-8, 379-388. | MR | Zbl
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