Chern Classes of Fibered Products of Surfaces
alg-geom
2008-02-03 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.alg-geom/9703017,
title = {Chern Classes of Fibered Products of Surfaces},
author = {Mina Teicher},
journal= {arXiv preprint arXiv:alg-geom/9703017},
year = {2008}
}
Comments
AMS-TeX, 12 pages, revised version. Appeared in Documenta