Chern Classes of Fibered Products of Surfaces

Details Chern Classes of Fibered Products of Surfaces Chern Classes of Fibered Products of Surfaces

1997-03-12

arxiv.org/abs/alg-geom/9703017v2

Mathematics

Algebraic Geometry

AMS-TeX, 12 pages, revised version. Appeared in Documenta

Scientific paper

In this paper we introduce a formula to compute Chern classes of fibered products of algebraic surfaces. For f, a generic projection to CP^2, of an algebraic surface X, we define X_k (for k smaller than degf) to be the k products of X over f minus the big diagonal. For k=degf, X_k is called the Galois cover of f w.r.t. full symmetric group. Let S be the branch curve of f. We give a formula for c_1^2 and c_2 of X_k, in terms of degf, degS, and the number of cusps, nodes and branch points of S. We apply the formula in 2 examples and add a conjecture concerning the spin structure of fibered products of Veronese surfaces.

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