Abstract

The classical hyperplane section theorem of Zariski about the fundamental groups of the complements to hypersurfaces in the complex projective space is generalized to the weighted homogeneous case. Using this result, we study how the fundamental group of the complement to a projective plane curve changes under covering of the projective plane by another projective plane. We also give an example of plane curves whose complements have nonabelian and finite fundamental groups. Few examples of such curves have been known. By the weighted Zariski's hyperplane section theorem, we can determine the group structure of these finite nonabelian groups.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 127-157
Launched on MUSE
1997-02-01
Open Access
No
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