L-infinity pairs and applications to singularities
Abstract
Over a field of characteristic zero, every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded Lie algebra together with a module. Unfortunately, these pairs are usually infinite-dimensional. We show that every deformation problem with cohomology constraints is controlled by a typically finite-dimensional L-infinity pair. As a first application, we show that for complex algebraic varieties with no weight-zero 1-cohomology classes, the components of the cohomology jump loci of rank one local systems containing the constant sheaf are tori. This imposes restrictions on the fundamental groups. The same holds for links and Milnor fibers.
Cite
@article{arxiv.1804.06672,
title = {L-infinity pairs and applications to singularities},
author = {Nero Budur and Marcel Rubió},
journal= {arXiv preprint arXiv:1804.06672},
year = {2019}
}
Comments
v2: the exposition on standard deformation theory is shortened, otherwise minor changes, final version to appear in Adv. Math