Surface classification and local and global fundamental groups, I

Details Surface classification and local and global fundamental groups, I Surface classification and local and global fundamental groups, I

2006-02-07

arxiv.org/abs/math/0602128v2

Mathematics

Algebraic Geometry

20 pages, to appear in the Rendiconti Accademia Lincei, new series, volume dedicated to the 90-th birthday of Guido Zappa. The

Scientific paper

Given a smooth complex surface S, and a compact connected global normal crossings divisor $D = \cup_i D_i$, we consider the local fundamental group, i.e., the fundamental group Gamma of T-D, where T is a good tubular neighbourhood of D. One has a surjection of Gamma onto the fundamental group of D, and the kernel $\sK$ is normally generated by geometric loops $\ga_i$ around the curve $D_i$. Among the main results, which are strong generalizations of a well known theorem of Mumford, is the nontriviality of $\ga_i$ in the local fundamental group, provided all the curves $D_i$ of genus zero have selfintersection <= -2. (in particular this holds if the canonical divisor is nef on D), and under the technical assumption that the dual graph of D is a tree.

Affiliated with

Also associated with

No associations

Rating

Surface classification and local and global fundamental groups, I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Surface classification and local and global fundamental groups, I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surface classification and local and global fundamental groups, I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63431