Around the tangent cone theorem
Algebraic Topology
2016-11-01 v2 Algebraic Geometry
Abstract
A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.
Cite
@article{arxiv.1502.02279,
title = {Around the tangent cone theorem},
author = {Alexander I. Suciu},
journal= {arXiv preprint arXiv:1502.02279},
year = {2016}
}
Comments
39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM series