Vector bundles and $SO(3)$ invariants for elliptic surfaces I

Details Vector bundles and $SO(3)$ invariants for elliptic surfaces I Vector bundles and $SO(3)$ invariants for elliptic surfaces I

1993-07-14

arxiv.org/abs/alg-geom/9307002v1

Mathematics

Algebraic Geometry

19 pages, AMS-TeX

Scientific paper

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney class is transverse to the unique primitive class $\kappa$ such that a positive multiple of $\kappa$ is the class of a general fiber on the surface. In this paper, we collect preliminary results on elliptic surfaces and vector bundles and give the general outline of the argument.

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