BASIC INTERSECTION THEORY ON THE MODULI SPACE OF CURVES

Let E be a vector bundle of rank r. To E, we associate the Chern polynomial c(E) = 1 + c1(E) + c2(E) + · · ·+ cr(E). The Chern roots of E are the formal roots of c(E), that is c(E) = r∏ i=1 (1 + αi). The Chern character of E is defined by ch(E) = r∑ i=1 eαi. Since the Chern character is symmetric in the Chern roots, it can be expressed in terms of the Chern classes. Simple manipulations with power series show that ch(E) = r + c1(E) + c21(E) − 2c2(E)