Projective varietes, linear systems and vector bundles PDF

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of ... For smooth projective varieties, Serre duality can be viewed as an analog of Poincaré duality. ... For example, the theory of holomorphic vector bundles (more generally coherent analytic ... it is called the complete linear system of D. In recent years, ideas and methods from the theory of vector bundles have been applied to ... The first is historical—the equations defining varieties have been ... smooth non-degenerate complex projective variety of degree d and dimension n,.