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/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to asrelative Ginzburg algebras, associated with marked surfaces equipped with adecomposition into $n$-gons ($n$-angulation). We relate their derivedcategories to the geometry of the surface. Results include the description of asubset of the objects in the derived categories in terms of curves in thesurfaces and their Homs in terms of intersections. The description of thesederived categories as the global sections of perverse schobers greatlyfacilitates the construction of these geometric models, as the constructionreduces to gluing local data. This approach may be considered as a generalized,algebraic analogue of matching sphere constructions appearing in the symplecticgeometry of Lefschetz fibrations. Most results also hold for the perverseschobers defined over any commutative ring spectrum.  As an application of the geometric model in the case $n=3$, we match certainExt-groups in the derived categories of these relative Ginzburg algebras andthe extended mutation matrices of a class of cluster algebras withcoefficients, associated to multi-laminated marked surfaces by Fomin-Thurston.

Geometric models for the derived categories of Ginzburg algebras of n-angulated surfaces via local-to-global principles