Let $X$ be a reduced projective curve over a field $k$.
Is there a bound on the number of irreducible components of $X$ in terms of its arithmetic genus $p_a(X) = 1- \chi_k(\mathcal{O}_X)$?
Or are those two invariants absolutely not related?
2026-03-25 17:21:54.1774459314
Is there a bound on the number of irreducible components in terms of the (arithmetic) genus?
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