Given pure-dimensional (generalized) cycles $\mu_1$ and $\mu_2$ on a projective manifold $Y$ we introduce an intrinsic product $\mu_1\diamond_{Y} \mu_1$ that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. % Given a very ample line bundle $L\to Y$ we define a product $\mu_1\bl \mu_2$ that also represents all the local intersection numbers and in addition, provided that $\mu_j$ are effective, satisfies a Bezout inequality... (read more)

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