On the most algebraic K3 surfaces and the most extremal log enriques surfaces

American Journal of Mathematics

Volumn 118, Issue 6, 1996, Pages 1277-1297

  Oguiso, Keiji ^a   Zhang, De Qi ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038273642     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. 2 for log surfaces, Internat. J. Math. 5 (1995), 779-810.
2. M. F. Atiyah and G. B. Segal, The index of elliptic operators: II, Ann. of Math. 87 (1968), 531-545.
3. M. F. Atiyah and I. M. Singer, The index of elliptic operators: III, Ann. of Math. 87 (1968), 546-604.
4. W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces, Springer-Verlag, New York, 1984.
5. R. Blache, The structure of 1.c. surfaces of Kodaira dimension zero, I, J. Algebraic Geom. 4 (1995), 137-179.
6. M. Kato and I. Naruki, Depth of rational double points on quartic surfaces, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), 72-75.
7. Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603-633.
8. D. Morrison, On K3 surfaces with large Picard number, Invent. Math. 75 (1984), 105-121.
9. V. Nikulin, On Kummer surfaces, Math. USSR-Izv. 9 (1975), 261-275.
10. _, Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections, J. Soviet Math. 22 (1983), pp. 1401-1475.
11. K. Oguiso, On Jacobian fibrations on the Kummer surfaces of the product of non-isogenous elliptic curves, J. Math. Soc. Japan 41 (1989), 651-680.
12. _, On algebraic fiber space structures on a Calabi-Yau 3-fold, Internat. J. Math. 4 (1993), 439-465.
13. _, On certain rigid fibered Calabi-Yau threefolds, Math. Z. 22 (1996), 437-448.
14. _, On fibred Calabi-Yau threefolds of quasi-product type, forthcoming.
15. K. Oguiso and D.-Q. Zhang, On the extremal log Enriques surfaces, II, preprint 1995.
16. M. Reid, Campedelli versus Godeaux, Problems in the Theory of Surfaces and their Classification, Trento, October 1988 (F. Catanese, et al., eds.), Academic Press, Boston, 1991, pp. 309-365.
17. T. Shioda and H. Inose, On singular K3 surfaces, Complex Analysis and Algebraic Geometry, Cambridge University Press, 1977, pp. 119-136.
18. É. B. Vinberg, The two most algebraic K3 surfaces, Math. Ann. 265 (1983), 1-21.
19. C. Voisin, Miroirs et involutions sur les surfaces K3, Astérisque 218 (1993), 273-323.
20. P. M. H. Wilson, The existence of elliptic fibre space structures on Calabi-Yau threefolds, Math. Ann. 300 (1994), 693-703.
21. D.-Q. Zhang, Logarithmic Enriques surfaces, J. Math. Kyoto Univ. 31 (1991), 419-466.
22. _, Logarithmic Enriques surfaces, II, J. Math. Kyoto Univ. 33 (1993), 357-397.
23. _, Quotients of K3 surfaces modulo involutions, preprint, 1995, submitted.
24. _, Normal algebraic surfaces with trivial two or four times of the canonical divisor, submitted, 1996.
25. _, Normal algebraic surfaces with trivial five times of the canonical divisor, preprint, 1996.
26. _, Normal algebraic surfaces with trivial three times of the canonical divisor, preprint, 1996.