We study the families of lines on the quintic threefolds of the pencil $x_0^5 + x_1^5 + x_2^5 + x_3^5 + x_4^5 - 5tx_0x_1x_2x_3x_4 = 0$. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone.
van Geemen's families of lines on special quintic threefolds.
ALBANO, Alberto;
1991-01-01
Abstract
We study the families of lines on the quintic threefolds of the pencil $x_0^5 + x_1^5 + x_2^5 + x_3^5 + x_4^5 - 5tx_0x_1x_2x_3x_4 = 0$. We show that on the generic threefold of the pencil there exists a 1-dimensional family of lines that is not a cone.
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