Is there a general way to have a plane curve be irreducible? If the curve $C \in \mathbb{C} [x,y]$, would it be sufficient for it to factor into linear terms? What about if I have an equation of the form $(a_1x+b_1y)^r$ and I want to add a non-constant term to make it irreducible over \mathbb{C}.
2026-05-05 02:23:41.1777947821
Is there a general way to have a polynomial in two variables over C (a plane curve) be irreducible?
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