Surface Classification

نویسنده

  • FABRIZIO CATANESE
چکیده

Given a smooth complex surface S, and a compact connected global normal crossings divisor D = ∪ i D i , we consider the local fundamental group π 1 (T \ D), where T is a good tubular neighbourhood of D. One has an exact sequence 1 → K → Γ := π 1 (T −D) → Π := π 1 (D) → 1, and the kernel K is normally generated by geometric loops γ 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 γ i in Γ = π 1 (T −D), provided all the curves D i of genus zero have selfintersection D 2 i ≤ −2 (in particular this holds if the canonical divisor K S is nef on D), and under the technical assumption that the dual graph of D is a tree.

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تاریخ انتشار 2006