"Non UBC"@en .
"DSpace"@en .
"Kuwata, Masato"@en .
"2018-07-23T05:01:36Z"@* .
"2018-01-23T10:37"@en .
"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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/66559?expand=metadata"@en .
"61 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Chuo University"@en .
"Banff (Alta.)"@en .
"10.14288/1.0369010"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Algebraic geometry"@en .
"Relativity and gravitational theory"@en .
"Mathematical physics"@en .
"Shioda-Inose structure and elliptic K3 surfaces with high Mordell-Weil rank"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/66559"@en .