Geodesic
Chern classes of fibered products of surfaces
Documenta mathematica, Tome 3 (1998), pp. 321-332
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In this paper we introduce a formula to compute Chern classes of fibered products of algebraic surfaces. For f:X→CP2 a generic projection of an algebraic surface, we define Xk​ for k≤n(n=degf) 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 c12​ 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 c12​/c2​. We pose conjectures concerning the spin structure of fibered products of Veronese surfaces and their fundamental groups.
DOI : 10.4171/dm/48
Classification : 14J10, 20F36
Mots-clés : surfaces, Chern classes, Galois covers, fibered product, generic projection, algebraic surface 
@article{10_4171_dm_48,
     author = {Mina Teicher},
     title = {Chern classes of fibered products of surfaces},
     journal = {Documenta mathematica},
     pages = {321--332},
     year = {1998},
     volume = {3},
     doi = {10.4171/dm/48},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/48/}
}
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Mina Teicher. Chern classes of fibered products of surfaces. Documenta mathematica, Tome 3 (1998), pp. 321-332. doi: 10.4171/dm/48

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