Deformations of free and linear free divisors
Michele Torielli
TL;DR
This paper studies how free and linear free divisors deform, introducing a complex to compute their deformation spaces, revealing that many such divisors have trivial deformation cohomology.
Contribution
It introduces a new complex for calculating deformation spaces of free divisors and analyzes their cohomology, providing new insights into their deformation theory.
Findings
Many linear free divisors have zero deformation cohomology.
The cohomology is constructible in many cases.
The complex effectively computes deformation spaces.
Abstract
We investigate deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates deformation spaces. This cohomology turns out to be zero for many linear free divisors and to be constructible in many cases
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory