English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

For a complex central essential hyperplane arrangement   $\mathcal{A}$  , let   $F_{\mathcal{A}}$   denote its Milnor fiber. We use Tevelev’s theory of tropical compactifications to study invariants related to the mixed Hodge structure on the cohomology of   $F_{\mathcal{A}}$  . We prove that the map taking an arrangement   $\mathcal{A}$   to the Hodge-Deligne polynomial of   $F_{\mathcal{A}}$   is locally constant on the realization space of any loop-free matroid. When   $\mathcal{A}$   consists of distinct hyperplanes, we also give a combinatorial description for the homotopy type of the boundary complex of any simple normal crossing compactification of   $F_{\mathcal{A}}$  . As a direct consequence, we obtain a combinatorial formula for the top weight cohomology of   $F_{\mathcal{A}}$  , recovering a result of Dimca and Lehrer.

Hyperplane Arrangements and Mixed Hodge Numbers of the Milnor Fiber