REPRESENTING CHARACTERISTIC HOMOLOGY CLASSES OF MCP(2)NUMBER-N(CP)OVER-BAR(2)

We prove the following theorems. Theorem 1. If m, n greater-than-or-eq ual-to 1, x is-an-element-of H-2(mCP2#nCP2BAR) is a characteristic hom ology class with x2 = 16l + m - n > 0 and (1) m < 3l + 1 provided l gr eater-than-or-equal-to > 0, or (2) m < -19l + 1 provided l < 0. Suppos e that the 1118-conjecture is true. Then x cannot be represented by a smoothly embedded 2-sphere. Theorem 2. Let m, n greater-than-or-equal- to 4l > 0, x is-an-element-of is-an-element-of H-2(mCP2#nCP2BAR) be a primitive characteristic homology class with x2 = +/-16l + m - n . The n x can be represented by a smoothly embedded 2-sphere.