Chern classes of fibered products of surfaces

zbMATH Open0923.14022arXivalg-geom/9703017MaRDI QIDQ1276546

Mina Teicher

Publication date: 7 February 1999

Published in: Documenta Mathematica (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/alg-geom/9703017

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zbMATH Keywords

fundamental groupsGalois coversfibered products of Veronese surfacesnon-diffeomorphic surfaces with same Chern class

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Families, moduli, classification: algebraic theory (14J10)

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