THE MODIFIED DIAGONAL CYCLE ON THE TRIPLE PRODUCT OF A POINTED CURVE

Let X be a curve over a field k with a rational point e. we define a canonical cycle Delta(e) is an element of Z(2)(X(3))(hom). Suppose that k is a number field and that X has semi-stable reduction over the integers of k with fiber components non-singular. we construct a regular model of X(3) and show that the height pairing [tau*(Delta(e)),tau'*(Delta(e))] is well defined where tau and tau' are corrsespondences. The paper ends with a brief discussion of heights and L-functions in the case that X is a modular curve.