# Chern classes of fibered products of surfaces

### Mina Teicher

## Abstract

In this paper we introduce a formula to compute Chern classes of fibered products of algebraic surfaces. For $f:X→CP_{2}$ a generic projection of an algebraic surface, we define $X_{k}$ for $k≤n(n=gf)$ to be the closure of $k$ products of $X$ over $f$ minus the big diagonal. For $k=n$ (or $n−1),X_{k}$ is called the full Galois cover of $f$ w.r.t. full symmetric group. We give a formula for $c_{1}$ and $c_{2}$ of $X_{k}.$ For $k=n$ the formulas were already known. We apply the formula in two examples where we manage to obtain a surface with a high slope of $c_{1}/c_{2}.$ We pose conjectures concerning the spin structure of fibered products of Veronese surfaces and their fundamental groups.

## Cite this article

Mina Teicher, Chern classes of fibered products of surfaces. Doc. Math. 3 (1998), pp. 321–332

DOI 10.4171/DM/48