Nodal degenerations of plane curves and Galois covers

Details Nodal degenerations of plane curves and Galois covers Nodal degenerations of plane curves and Galois covers

2004-11-15

arxiv.org/abs/math/0411328v1

Mathematics

Algebraic Geometry

16 pages, 3 figures

Scientific paper

Globally irreducible nodes (i.e. nodes whose branches belong to the same irreducible component) have mild effects on the most common topological invariants of an algebraic curve. In other words, adding a globally irreducible node (simple nodal degeneration) to a curve should not change them a lot. In this paper we study the effect of nodal degeneration of curves on fundamental groups and show examples where simple nodal degenerations produce non-isomorphic fundamental groups and this can be detected in an algebraic way by means of Galois coverings.

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