Abstract
This chapter presents a construction method of algebraic vector bundles on noetherian schemes X by analyzing the results. It is a geometric method because algebraic vector bundles can be constructed using closed subschemes of X and it might be a canonical generalization of the method to construct regular vector bundles obtained by Maruyama. The notion of invertibility of effective Weil divisors along the normal Cartier divisors of X plays a key role in the construction method. If X is a nonsingular quasi-projective variety defined over an algebraically closed field, then every algebraic vector bundle on X up to tensoring a line bundle is obtained by the construction method that is discussed in the chapter. The chapter explains the Horrocks–Mumford bundle from the point of view of elementary transformations of algebraic vector bundles.
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