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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We define the counting of holomorphic cylinders in log Calabi-Yau surfaces.Although we start with a complex log Calabi-Yau surface, the counting isachieved by applying methods from non-archimedean geometry. This gives rise tonew geometric invariants. Moreover, we prove that the counting satisfies aproperty of symmetry. Explicit calculations are given for a del Pezzo surfacein detail, which verify the conjectured wall-crossing formula for thefocus-focus singularity. Our holomorphic cylinders are expected to give ageometric understanding of the combinatorial notion of broken line by Gross,Hacking, Keel and Siebert. Our tools include Berkovich spaces, tropicalgeometry, Gromov-Witten theory and the GAGA theorem for non-archimedeananalytic stacks.

Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I