Kummer sandwich theorem of certain elliptic K3 surfaces

Proceedings of the Japan Academy Series A: Mathematical Sciences

Volumn 82, Issue 8, 2006, Pages 137-140

  Shioda, Tetsuji ^a  

^a RIKKYO UNIVERSITY   (Japan)

Author keywords

Elliptic surface; Isogeny; K3 surface; Kummer surface; Singular fibres

Indexed keywords

EID: 33750813532     PISSN: 03862194     EISSN: 03862194     Source Type: Journal    
DOI: 10.3792/pjaa.82.137     Document Type: Conference Paper

References (13)

1. H. Inose, Defining equations of singular K3 surfaces and a notion of isogeny, in Proceedings of the International Symposium on Algebraic Geometry (Kyoto 1977), 495-502, Kinokuniya Book Store, Tokyo, 1978.
2. H. Inose and T. Shioda, On singular K3 surfaces, in Complex Analysis and Algebraic Geometry, Iwanami Shoten, Tokyo, Cambridge Univ. Press, Cambridge-New York, 1977, pp.119-136.
3. K. Kodaira, On compact analytic surfaces 11-111, Ann. of Math. (2) 77 (1963), 563-626;
4. K. Kodaira, Ann. of Math. (2) ibid. 78 (1963), 1-40;
5. in Collected Works, 3, Iwanami Shoten, Tokyo, Princeton Univ. Press, Princeton, 1975, pp.1269-1372.
6. M. Kuwata, Elliptic K3 surfaces with given Mordell-Weil rank, Comment. Math. Univ. St. Pauli 49 (2000), 91-100.
7. M. Kuwata and T. Shioda, Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface. (Submitted).
8. D. Morrison, On K3 surfaces with large Picard number, Invent. Math. 75 (1984), 105-121.
9. 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.
10. I. Piateckii-Shapiro and I. R. Shafarevich, A Torelli theorem for algebraic surfaces of type K3, Math. USSR, Izv. 5 (1971), 547-587.
11. T. Shioda, A note on K3 surfaces and sphere packings, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), 68-72.
12. T. Shioda, Correspondence of elliptic curves and Mordell-Weil lattices of certain elliptic K3 surfaces, in Proceedings Algebraic Cycles (Leiden, 2004), Cambridge Univ. Press, Cambridge, (to appear).
13. J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, SLN 476 (1975), 33-52.