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 investigate the Cox ring of a normal complete variety X with algebraictorus action. Our first results relate the Cox ring of X to that of a maximalgeometric quotient of X. As a consequence, we obtain a complete description ofthe Cox ring in terms of generators and relations for varieties with torusaction of complexity one. Moreover, we provide a combinatorial approach to theCox ring using the language of polyhedral divisors. Applied to smoothk*-surfaces, our results give a description of the Cox ring in terms ofOrlik-Wagreich graphs. As examples, we explicitly compute the Cox rings of allGorenstein del Pezzo k*-surfaces with Picard number at most two and the Coxrings of projectivizations of rank two vector bundles as well as cotangentbundles over toric varieties in terms of Klyachko's description.

The Cox ring of an algebraic variety with torus action