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arXiv · 1512.03191

Complex $\text{G}_2$ and Associative Grassmannian

Selman Akbulut·Mahir Bilen Can
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Abstract

We obtain defining equations of the smooth equivariant compactification of the Grassmannian of the complex associative $3$-planes in $\C^7$, which is the parametrizing variety of all quaternionic subalgebras of the algebra of complex octonions $\OO\cong \C^8$. By studying the torus fixed points, we compute the Poincar\'e polynomial of the compactification.

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Selman Akbulut, Mahir Bilen Can. 2015-12-10. Complex $\text{G}_2$ and Associative Grassmannian. https://arxiv.org/abs/1512.03191

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