COMPLEX VARIABLES

By PATRICIA GONZALEZ

1 HOLOMORPHIC FUNCTIONS 1 2 LOCAL THEORY 8 3 A LITTLE HOMOLOGICAL ALGEBRA 13 4 LOCAL THEORY OF VARIETIES 22 5 THE NULLSTELLENSATZ 28 6 DIMENSION 44 7 COMPLETION OF LOCAL RINGS 52 8 SHEAVES 61 9 SHEAF COHOMOLOGY 69 10 COHERENT ALGEBRAIC SHEAVES 85 11 DOLBEAULT COHOMOLOGY 97 12 COHERENT ANALYTIC SHEAVES 104 13 PROJECTIVE VARIETIES 114 14 ALGEBRAIC VS ANALYTIC SHEAVES SERRE S THEOREMS 122 15 STEIN SPACES 134 16 FR CHET SHEAVES CARTAN S THEOREMS 147 17 THE BOREL WEIL BOTT THEOREM 164