Teicher, Mina

Chern classes of fibered products of surfaces

Doc. Math., J. DMV 3, 321-332 (1998)


Summary: In this paper we introduce a formula to compute Chern classes of fibered products of algebraic surfaces. For $f: X\to \CPt$ a generic projection of an algebraic surface, we define $X_k$ for $k\le n(n=\deg f) $ 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 $c_1^2$ 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 $c_1^2/c_2.$ We pose conjectures concerning the spin structure of fibered products of Veronese surfaces and their fundamental groups.

Mathematics Subject Classification

20F36, 14J10


surfaces, Chern classes, Galois covers, fibered product, generic projection, algebraic surface