Chern Classes of Fibered Products of Surfaces

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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 Xk for k ≤ 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), Xk is called the full Galois cover of f w.r.t. full symmetric group. We give a formula for c 2 1 and c2 of Xk. 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 2 1 /c2. We pose conjectures concerning the spin structure of fibered products of Veronese surfaces and their fundamental groups. 0. Introduction. When regarding an algebraic surface X as a topological 4-manifold, it has the Chern classes c 2 1, c2 as topological invariants. These Chern classes satisfy: c 2 1, c2 ≥ 0 5c 2 1 ≥ c2 − 36
Original languageAmerican English
Pages (from-to)321-342
JournalDocumenta Mathematica
Volume3
StatePublished - 1999

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