On the string-theoretic Euler number of a class of absolutely isolated singularities

Manuscripta Mathematica

Volumn 105, Issue 2, 2001, Pages 143-174

  Dais, Dimitrios I ^a  

^a UNIVERSITY OF IOANNINA   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035628351     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/pl00005875     Document Type: Article

References (30)

1. Batyrev, V.V.: Stringy Hodge numbers of varieties with Gorenstein canonical singularities. In: "Integrable Systems and Algebraic Geometry", Proceedings of the Taniguchi Symposium 1997, Eds. M.-H. Saito, Y. Shimizu & K. Ueno; Singapore: World Scientific, 1998, pp. 1-32
2. Batyrev, V.V.: Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. J. the European Math. Soc. 1, 5-33 (1999)
3. Batyrev, V.V., Borisov, L.A.: Mirror duality and string-theoretic Hodge numbers. Inventiones Math. 126, 183-203 (1996)
4. Batyrev, V.V., Cox. D.: On the Hodge structure of projective hypersurfaces in toric varieties. Duke Math. J. 75, 293-338 (1994)
5. Batyrev, V.V., Dais, D.I.: Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Topology 35, 901-929 (1996)
6. Chen, B.-Y., Ogiue, K.: Some implications of the Euler-Poincaré characteristic for complete intersection manifolds. Proc. of the A.M.S. 44, 1-8 (1974)
7. Dais, D.I., Roczen, M.: On the string-theoretic Euler number of 3-dimensional A-D-E singularities. Preprint, math.AG/0011117v2
8. Deligne, P.: Théorie de Hodge III. Publ. Math. I.H.E.S. 44, 5-77 (1975)
9. Denef, J., Loeser, F.: Motivic integration, quotient singularities and the Mckay correspondence. Preprint, math.AG/9903187
10. Dimca, A.: Topics on Real and Complex Singularities. Vieweg Advanced Lectures in Math., 1987
11. Dimca, A.: Singularities and Topology of Hypersurfaces. Universitext, Berlin-Heidelberg-New York: Springer-Verlag, 1992
12. Dolgachev, I.: Weighted projective varieties. In: "Group actions and vector fields", Proc. of Polish-North. Amer. Seminar, Vancouver 1981, Lecture Notes in Math., Vol. 956, Berlin-Heidelberg-New York: Springer-Verlag, 1982, pp. 34-71
13. Goryunov, V.V.: Symmetric quartics with many nodes. In: "Singularities and Bifurcations", Advances in Soviet Math., Vol. 21, AMS, 147-161 (1994)
14. Griffiths, P.: On the periods of certain rational integrals I, II. Ann. of Math. 90, 460-495 and 498-541 (1969)
15. Griffiths, P., Harris, J.: Principles of Algebraic Geometry. New York: J. Wiley & Sons, 1978
16. Hamm, H.: Zum Homotopietyp Steinscher Räume. Journal für die reine und angew. Math. 338, 121-135 (1983)
17. Hamm, H.: Hodge numbers for isolated singularities of non-degenerate complete intersections. In: "Singularities (The Brieskorn Anniversary Volume)", Eds. V.I. Arnold, G.-M. Greuel, J.H.M. Steenbrink, Progress in Math., Vol. 162, Boston-Basel: Birkhäuser, 1998, pp. 37-60
18. Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. of Math. 79, 109-326 (1964)
19. Hirzebruch, F.: Der Satz von Riemann-Roch in faisceau-theoretischer Formulierung. In: Proc. International Congress of Math. 1954, Vol. III, pp. 457-473. (See also: "Gesammelte Abhandlungen", Bd. I, Berlin-Heidelberg-New York: Springer-Verlag, 1987, pp. 128-144)
20. Hirzebruch, F.: Der Satz von Riemann-Roch in faisceau-theoretischer Formulierung. In: Proc. International Congress of Math. 1954, Vol. III, pp. 457-473. (See also: "Gesammelte Abhandlungen", Bd. I, Berlin-Heidelberg-New York: Springer-Verlag, 1987, pp. 128-144)
21. Hirzebruch, F : Arrangements of lines and algebraic surfaces. In "Arithmetic and Geometry II", Progress in Math., Vol. 36, Boston-Basel: Birkhäuser, 1983, pp. 113-140 (See also: "Gesammelte Abhandlungen", Bd. II, Berlin-Heidelberg-New York: Springer-Verlag, 1987, pp. 679-706)
22. Hirzebruch, F : Arrangements of lines and algebraic surfaces. In "Arithmetic and Geometry II", Progress in Math., Vol. 36, Boston-Basel: Birkhäuser, 1983, pp. 113-140 (See also: "Gesammelte Abhandlungen", Bd. II, Berlin-Heidelberg-New York: Springer-Verlag, 1987, pp. 679-706)
23. Hirzebruch, F: Some examples of threefolds with trivial canonical bundle. "Gesammelte Abhandlungen", Bd. II, Berlin-Heidelberg-New York: Springer-Verlag, 1987, pp. 757-770
24. Hunt, B.: Coverings and ball quotients with special emphasis on the 3-dimensional case. Bonner Mathematische Schriften, Bd. 174 (1986)
25. Knörrer, H.: Isolierte Singularitäten von Durchschnitten zweier Quadriken. Bonner Mathematische Schriften, Bd. 117 (1980)
26. Milnor, J.: Singular Points of Complex Hypersurfaces. Annals of Math. Studies, Vol. 61, Princeton, NJ: University Press, 1968
27. Reid M.: Canonical threefolds. Journée de Géométrie Algébrique d'Angers, A. Beauville ed., Sijthoff and Noordhoff, Alphen aan den Rijn, 1980, pp. 273-310
28. Steenbrink, J.H.M.: Intersection form for quasi-homogeneous singularities. Compositio Math. 34, 211-223 (1977)
29. Steenbrink, J.H.M.: Mixed Hodge structures associated with isolated singularities. In: Proc. of Symposia in Pure Math., Vol. 40, Part II, Providence, RI: AMS, 1983, pp. 513-536
30. 1 = 0, (with an appendix by B. van Geemen), Math. Z. 203, 211-225 (1990)