I'm studying characteristic classes from the Chern-Weil construction (via connection and curvature). I'm trying to compute some simple examples. Let $E$ be the tautological line bundle over projective space $P(\mathbf{C}^n)$. I want to show that the first Chern class of $E$ does not vanish. I suppose I could just introduce a connection on $E$ using local trivializations (is there a natural choice?), patch things together, compute the curvature and from this the first Chern class. However, that sounds a bit tedious. Are there more elegant ways to compute it?
2026-03-27 10:34:25.1774607665
Chern class of tautological line bundle
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