Geodesic
Chern classes of fibered products of surfaces
Documenta mathematica, Tome 3 (1998), pp. 321-332.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 20F36, 14J10
Keywords: surfaces, Chern classes, Galois covers, fibered product, generic projection, algebraic surface 
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     author = {Teicher, Mina},
     title = {Chern classes of fibered products of surfaces},
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     volume = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a3/}
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Teicher, Mina. Chern classes of fibered products of surfaces. Documenta mathematica, Tome 3 (1998), pp. 321-332. http://geodesic.mathdoc.fr/item/DOCMA_1998__3__a3/