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Description
The Cox ring of an algebraic variety is a graded algebra whose homogeneous components consist of the global sections of the line bundles on the variety. Cox rings play a central role in algebraic geometry, as their algebraic structure encodes substantial information about the (birational) geometry of the underlying variety. Despite their importance, providing explicit descriptions of Cox rings remains a challenging and often elusive problem.
In this talk, we will explore (hopefully through various examples) several techniques and results aimed at describing Cox rings in terms of other algebraic structures: cluster algebras their generalizations.
