Applications of braid group techniques to the decomposition of moduli spaces, new examples (Q1361373)

In this paper, the authors discuss constructions of examples of pairs of minimal surfaces of general type (with positive signature) which have the same Chern numbers \(c^2_1\), \(c_2\), but different fundamental groups. In their main examples of such pairs, one fundamental group can be an arbitrarily large finite abelian elementary 2-group, while the other one is trivial. These examples are obtained from Hirzebruch surfaces \(X\) specifically embedded in projective spaces by taking ``Galois covers with respect to the full symmetric group'' of their generic projections \(f:X\to \mathbb{P}^2\). The Chern numbers are calculated by Miyaoka's method, while the fundamental groups are computed from braid monodromy data around the complement of the branch curve in the plane.