Browsing Student Works by Author "Brooke, Corey"

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Lines and Conics in a Family of Quartic Surfaces

Richter, Karl (University of Oregon, 2023-05)

This thesis is primarily concerned with the fact that the general quartic surface does not contain a line or a conic section. More formally, the set of quartic surfaces containing lines or conic sections has measure ...
Lines on Cubic Threefolds and Fourfolds Containing a Plane

Brooke, Corey (University of Oregon, 2024-01-09)

This thesis describes the Fano scheme $F(Y)$ of lines on a general cubic threefold $Y$ containing a plane over a field $k$ of characteristic different from $2$. One irreducible component of $F(Y)$ is birational (over $k$) ...