Algebraic computation in geometry

Computations with algebraic curves and surfaces are very well suited for being treated with computer algebra. Many aspects of computer algebra need to be combined for successfully solving problems in this area, e.g. computations with algebraic coefficients, solution of algebraic equations and elimination theory, and derivation of power series approximations of branches. We will describe the application of computer algebra to problems arising in algebraic geometry. The program system CASA, which has been developed by the author and a group of students will be introduced.