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1 Sentences With "given variety to"

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Then multiplying a global section of O(D) by a nonzero scalar in k does not change its zero locus. As a result, the projective space of lines in the k-vector space of global sections H0(X, O(D)) can be identified with the set of effective divisors linearly equivalent to D, called the complete linear system of D. A projective linear subspace of this projective space is called a linear system of divisors. One reason to study the space of global sections of a line bundle is to understand the possible maps from a given variety to projective space. This is essential for the classification of algebraic varieties.

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