Common zero-locus of a family of polynomials: for S ⊆ k[x₁,…,x_n], V(S) = {p ∈ k^n : f(p) = 0 for all f ∈ S}. Equivalently, V(I) where I = (S) is the ideal generated by S. An affine variety is irreducible (not a proper union of two…
Common zero-locus of a family of polynomials: for S ⊆ k[x₁,…,x_n], V(S) = {p ∈ k^n : f(p) = 0 for all f ∈ S}. Equivalently, V(I) where I = (S) is the ideal generated by S. An affine variety is irreducible (not a proper union of two…