Iversen’s Formula for the Second Chern Classes of Regular Surfaces in Any Characteristic

The formula mentioned in the title is proved. Introduction Let S, T be complete nonsingular surfaces over an algebraically closed field k of any characteristic, and let h : T → S be a finite separable morphism of degree n. We establish a formula that expresses the Euler characteristic (understood as the degree of the second Chern class ∫ c2,T ) of T via the Euler characteristic of S and some local terms associated with components of the branch divisor Bh = hRh of h and with certain points on Bh (here Rh is the ramification divisor). Let Bh = ∑ i biBi, where the Bi are prime divisors on S. Then χT − nχS = ∑