Cox Rings of Trinomial Hypersurfaces

O. K. Kruglov

Lomonosov Moscow State University

Abstract: A criterion for the total coordinate space of a trinomial hypersurface to be a hypersurface is found. An algorithm for calculating the Cox ring in explicit form is proposed, and criteria for the total coordinate space to be rational and factorial are obtained.

Keywords: affine variety, torus action, Cox ring, polyhedral divisor, rational variety.

UDC: 512.718

Received: 05.06.2020

DOI: 10.4213/mzm12807

 English version: Mathematical Notes, 2021, 109:6, 884–895

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