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Toric variety

Orbit-cone correspondence

{title2=$V(\sigma)$}

For $\sigma\in\Sigma$, the closure of its torus orbit is
$$
V(\sigma)=\overline{O(\sigma)}
=\bigcup_{\tau\supseteq\sigma}O(\tau).
$$
Thus orbit-closure inclusion reverses face inclusion.


Orbit closure in a toric variety

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 152 / 1 / b / Solution

Orbit closure in a toric variety ( $V (σ)$ )

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