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 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

Zendy Tools

Zendy Open

In this paper we investigate the algebraic geometric nature of a solution ofthe Yang-Baxter equation based on the quantum deformation of the centrallyextended $sl(2|2)$ superalgebra proposed by Beisert and Koroteev \cite{BEKO}.We derive an alternative representation for the $\mathrm{R}$-matrix in whichthe matrix elements are given in terms of rational functions depending onweights sited on a degree six surface. For generic gauge the weights geometryare governed by a genus one ruled surface while for a symmetric gauge choicethe weights lie instead on a genus five curve. We have written down thepolynomial identities satisfied by the $\mathrm{R}$-matrix entries needed touncover the corresponding geometric properties. For arbitrary gauge the$\mathrm{R}$-matrix geometry is argued to be birational to the direct product$\mathbb{CP}^1 \times \mathbb{CP}^1 \times \mathrm{A}$ where $\mathrm{A}$ is anAbelian surface. For the symmetric gauge we present evidences that thegeometric content is that of a surface of general type lying on the so-calledSeveri line with irregularity two and geometric genus nine. We discusspotential geometric degenerations when the two free couplings are restricted tocertain one-dimensional subspaces.

Algebro-Geometric approach for a centrally extended U_q[sl(2|2)] R-matrix