Let $X$ be a 2-dimensional complex manifold, $C\subset X$ be a compact, reduced irreducible divisor. let $\nu: \tilde{C}\to C$ be a normalization(In this situation,$\tilde{C}$ is a riemann surface.).How to show that$H^2(C,\mathbb{Z})\cong H^2(\tilde{C},\mathbb{Z})\cong \mathbb{Z}$?
2026-03-27 18:09:23.1774634963
Normalization of curve and integral cohomology
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