Advanced Studies in Pure Mathematics

Homotopy groups of complements to ample divisors

Anatoly Libgober

Full-text: Open access

Abstract

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

Source
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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546543236

Digital Object Identifier
doi:10.2969/aspm/04310179

Mathematical Reviews number (MathSciNet)
MR2325138

Zentralblatt MATH identifier
1134.14014

Citation

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. https://projecteuclid.org/euclid.aspm/1546543236


Export citation