1. CMB 2007 (vol 50 pp. 215)
|Elliptic $K3$ Surfaces with Geometric Mordell--Weil Rank $15$ |
We prove that the elliptic surface $y^2=x^3+2(t^8+14t^4+1)x+4t^2(t^8+6t^4+1)$ has geometric Mordell--Weil rank $15$. This completes a list of Kuwata, who gave explicit examples of elliptic $K3$-surfaces with geometric Mordell--Weil ranks $0,1,\dots, 14, 16, 17, 18$.
Categories:14J27, 14J28, 11G05
2. CMB 2003 (vol 46 pp. 546)
|$L$-Series of Certain Elliptic Surfaces |
In this paper, we study the modularity of certain elliptic surfaces by determining their $L$-series through their monodromy groups.
3. CMB 2000 (vol 43 pp. 174)
|Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces |
We show that the use of orbifold bundles enables some questions to be reduced to the case of flat bundles. The identification of moduli spaces of certain parabolic bundles over elliptic surfaces is achieved using this method.
Categories:14J27, 32L07, 14H60, 14D20