Notation (1) N = (2) Z = (3) Q = (4) R = (5) C = (6) R = (7) C = If p G N and 5 is a set, then (8) S* (9) # 5 If a G R, 6 G R, and T C 1, then the positive integers the integers the rational numbers the real numbers the complex numbers RU{-oo,+oo} C U {oo} = Pi, the Riemann sphere = S x ... x S (p-times) = card 5, the number of elements of S (10) I T[a, b] = {x G T\a x b} ii. T(a, b] = {x G T\a x b} T[a,b) = {xeT\axb} T(a, b) = {x G T\a x 6} in. iv. For pGZ+ , (11) i. T + = T(0,+oo] ii. T+ = T[0,+oo] Hi. T~ = T[-oo,0) iv. T- = T[-oo,0] (12) V = ( ^ ) ( - l ) " ^ " P i If M is a complex manifold of dimension m, then (13) i. T(M) = the holomorphic tangent bundle of M ii. T*(M) = the holomorphic cotangent bundle of M Hi. T(M) = the conjugate of X(M) iv. T*(M) = the conjugate of X*(M) v. A T*(M) = the canonical bundle of M, denoted X M or K IX

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