I have a holomorphic map $f: C \to X$ where $\dim_\mathbb{C}C=1$ and $\dim_\mathbb{C}X=2$. Why is $\text{deg}\det f^*TX=-c_1(X)\cdot[C]$? I'm really curious to how that negative sign shows up.
2026-03-30 01:30:06.1774834206
degree of determinant line bundle of pullback in terms of Chern class
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