Complex G₂ and Associative Grassmannian
classification
🧮 math.AG
math.DGmath.RT
keywords
complexassociativecompactificationgrassmannianalgebracomputecongdefining
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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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