Here the \( f_i \in k[X_1 ,...,X_n ] \) are polynomials in n variables with coefficients in a field k. The set of solutions is a subset \( V(f_1 ,...,f_r ) \) of \( k^n \). Polynomial equations are omnipresent in and outside mathematics, and have been studied since antiquity. The focus of algebraic geometry is studying the geometric structure of their solution sets.
KeywordsVector Bundle Line Bundle Projective Space Algebraic Geometry Commutative Ring
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