Non UBC
DSpace
Kuwata, Masato
2018-07-23T05:01:36Z
2018-01-23T10:37
If two $K3$ surfaces $X$ and $Y$ over $\mathbb{C}$ admit a rational map of finite degree $X\to Y$, Inose proved that their Picard numbers $\rho(X)$ and $\rho(Y)$ are equal. Suppose $X$ admits an elliptic fibration $\pi:X\to \mathbf{P}^{1}$. By a base change $b:\mathbf{P}^{1}\to \mathbf{P}^{1}$, we obtain another elliptic surface $\pi\times b:X':=X\times_{\mathbf{P}^{1}}\mathbf{P}^{1}\to \mathbf{P}^{1}$. If $X'$ is once again a $K3$ surface, we know $\rho(X')=\rho(X)$. However, it is difficult in general to find generators of the N\'eron-Severi goup of $X'$. Starting from various $K3$ surfaces $X$ having a Shioda-Inose structure, we construct $X'\to \mathbf{P}^{1}$ whose Mordell-Weil rank is large, and explore methods of finding generators of the Mordell-Weil group.
https://circle.library.ubc.ca/rest/handle/2429/66559?expand=metadata
61 minutes
video/mp4
Author affiliation: Chuo University
Banff (Alta.)
10.14288/1.0369010
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Algebraic geometry
Relativity and gravitational theory
Mathematical physics
Shioda-Inose structure and elliptic K3 surfaces with high Mordell-Weil rank
Moving Image
http://hdl.handle.net/2429/66559