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Non‐complete rational T ‐varieties of complexity one
Author(s) -
Hausen Jürgen,
Wrobel Milena
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600009
Subject(s) - mathematics , invertible matrix , affine transformation , homogeneous , torus , constant (computer programming) , pure mathematics , action (physics) , ring (chemistry) , algebra over a field , discrete mathematics , combinatorics , geometry , computer science , chemistry , physics , organic chemistry , quantum mechanics , programming language
We consider rational varieties with a torus action of complexity one and extend the combinatorial approach via the Cox ring developed for the complete case in earlier work to the non‐complete, e.g. affine, case. This includes in particular a description of all factorially graded affine algebras of complexity one with only constant homogeneous invertible elements in terms of canonical generators and relations.