Let $X=\mathbb{C}^n/\Lambda$ be a compact complex torus, where $\Lambda \subset \mathbb{C}^n$ is a lattice acting on $\mathbb{C}^n$ by translations. Then the holomorphic tangent bundle $T^{1,0}X$ is holomorphically trivial. More precisely, there is a holomorphic vector bundle isomorphism
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\begin{align*}
X \times \mathbb{C}^n \cong T^{1,0}X.
\end{align*}
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Consequently, the Chern classes of the holomorphic tangent bundle satisfy