Chern classes of fibered products of surfaces

  • Mina Teicher

Chern classes of fibered products of surfaces cover
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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\CPtf: X\to \CPt a generic projection of an algebraic surface, we define XkX_k for kn(n=degf)k\le n(n=\deg f) to be the closure of kk products of XX over ff minus the big diagonal. For k=nk=n (or n1),Xkn-1), X_k is called the full Galois cover of ff w.r.t. full symmetric group. We give a formula for c12c_1^2 and c2c_2 of Xk.X_k. For k=nk=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.c_1^2/c_2. We pose conjectures concerning the spin structure of fibered products of Veronese surfaces and their fundamental groups.

Cite this article

Mina Teicher, Chern classes of fibered products of surfaces. Doc. Math. 3 (1998), pp. 321–332

DOI 10.4171/DM/48