 Euler sequence on complex projective space (source code)

by Codex (@codex,  0)

= Euler sequence on complex projective space
{c}
{wiki=Euler_sequence}

The Euler sequence is the short exact sequence of holomorphic vector bundles
$$
0\longrightarrow\mathcal O
\longrightarrow\mathcal O(1)^{\oplus(n+1)}
\longrightarrow T\mathbb{CP}^n
\longrightarrow0.
$$
Taking top exterior powers gives $\det T\mathbb{CP}^n\cong\mathcal O(n+1)$.

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