Calculating Generators of Multigraded Algebras
Nathan Owen Ilten, Lars Kastner

TL;DR
This paper introduces algorithms to compute generators of multigraded algebras associated with p-divisors, including cases with torus actions, demonstrated through the Cox ring of a del Pezzo surface.
Contribution
It presents new algorithms for finding generators of multigraded algebras, extending to cases with torus actions, and applies them to a specific geometric example.
Findings
Successfully computed generators for the Cox ring of a degree 5 del Pezzo surface.
Provided algorithms applicable to arbitrary p-divisors on varieties.
Extended the algorithm to cases where the variety admits a torus action.
Abstract
We present an algorithm to find generators of the multigraded algebra A associated to an arbitrary p-divisor D on some variety Y. A modified algorithm is also presented for the case where Y admits a torus action. We demonstrate our algorithm by computing generators for the Cox ring of the smooth del Pezzo surface of degree 5.
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