Year: 2026
Type: preprint
Abstract: We extend the dual complex of a simple normal crossings divisor to a homotopy type invariant $\mathcal{D}(X)$ of arbitrary complex varieties, and we prove that it is contractible when $X$ is connected and of klt type. In fact, the dual complex belongs to a broader class of invariants, which we call RC (rationally connected)-invariant functors. We prove a rigidity theorem governing the behavior of such functors with respect to rationally connected fibrations.
Source: arXiv (Cornell University)
Author: Burke, Andrew
Institution: Harvard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223364048