Advanced Studies in Pure Mathematics

Homotopy groups of complements to ample divisors

Anatoly Libgober

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Homotopy groups of the complements to divisors with ample components on non-singular projective varieties are considered as the modules over the fundamental group. We prove a vanishing theorem and consider the calculation of supports of these modules by relating them to the cohomology of local systems. We review previous work on the local study of isolated non-normal crossings. As an application, we obtain information about the support loci of homotopy groups of arrangements of hyperplanes.

Article information

Singularity Theory and Its Applications, S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimada and T. Sano, eds. (Tokyo: Mathematical Society of Japan, 2006), 179-204

Received: 23 March 2004
Revised: 12 September 2004
First available in Project Euclid: 3 January 2019

Permanent link to this document euclid.aspm/1546543236

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Libgober, Anatoly. Homotopy groups of complements to ample divisors. Singularity Theory and Its Applications, 179--204, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04310179.

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