Dmitri A. Timashev Torus actions of complexity one Let T = (Cв )r be a complex algebraic torus acting on an algebraic variety X . ... By Sumihiro's theorem X = Xi is covered by finitely many affine open T -stable subvarieties. ... The normal affine T -varieties of complexity 1 are in a 11 correspondence with the hypercones. ... Conclusion: Normal T -varieties of complexity 1 are in a 11 correspondence with finite collections of hypercones intersecting in their common hyperfaces, called hyperfans. ...
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