Much of the development of the main stream of algebraic geometry in the 20th century occurred within an abstract algebraic framework , with increasing emphasis being placed on `` intrinsic '' properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space ; this parallels developments in topology , differential and complex geometry .
Much of the development of the main stream of algebraic geometry in the 20th century occurred within an abstract algebraic framework , with increasing emphasis being placed on `` intrinsic '' properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space .