On torus actions of higher complexity

Abstract

We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of general arrangement varieties and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.

arXiv commentBackground, examples and references added, more self-contained presentation, 54 pages

References in corpus (11)

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Cited by in corpus (8)

• On smooth Fano fourfolds of Picard number two
• On the anticanonical complex
• The anticanonical complex for non-degenerate toric complete intersections
• On Fano threefolds with ${\mathbb{C}}^{\ast }$-action
• The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
• Classifying log del Pezzo surfaces with torus action
• Del Pezzo surfaces of Picard number one admitting a torus action
• The automorphism group of a rational projective k*-surface