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April 06, 2022
Wednesday, April 06
Transformation Groups Seminar
Time: 10:30
Speaker: Kumar Shukla (Western)
Title: "Counting Lines in a Cubic Surface using Localization Formula"
Room: MC 204

Abstract: By a cubic surface in $\mathbb{CP}^3$, we mean the zero set of a homogenous degree 3 polynomial in 4 variables. Cayley computed the number of lines on a 'generic' cubic surface to be 27. This number can be computed as the integral of the Euler class of a certain bundle over the Grassmannian $G(2, 4)$ of lines in $\mathbb{CP}^3$. To evaluate this integral, we observe that there is a certain action of 4-torus on $G(2, 4)$, and then we apply the Atiyah-Bott localization formula.