Polyhedral divisors and algebraic torus actions

By K. Altmann, Jürgen Hausen. 2003

67 citations recorded by the source corpus.

We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, and it comprises the theory of affine toric varieties.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c35ebe0af4e4859cbc9b4a1e4d8ab5dc6d30a9c2

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In Geometry and Topology

1. Tristan C. Collins
2. G'abor Sz'ekelyhidi
3. Chi Li
4. Hendrik Suss
5. Nathan Owen Ilten
6. Jürgen Hausen
7. Thibaut Delcroix
8. Jian Song

In Mathematical Physics

1. Hendrik Suss
2. Tristan C. Collins
3. G'abor Sz'ekelyhidi
4. Jürgen Hausen
5. Abdellah Lahdili
6. Adam Jacob
7. Kento Fujita
8. Mattias Jonsson

In Statistical and Nonlinear Physics

1. Tristan C. Collins
2. G'abor Sz'ekelyhidi
3. Hendrik Suss
4. Jürgen Hausen

Citations in the corpus

• Sasaki–Einstein metrics and K–stability (2015, methodology): “Using the techniques of [1] we can describe this fibration in terms of combinatorial data called a p-divisor.”
• The Cox ring of an algebraic variety with torus action (2009, background): “By Lemma 3.1, the function f ′ is invariant under every Gi and thus under G0.”
• K-stability for Fano manifolds with torus action of complexity $1$ (2015, background): “table. In particular, Xis K¨ahler-Einstein if and only if Xis equivariantly K-stable. 3. Polyhedral divisors and divisorial polytopes In this section, we recall notions related to polyhedral divisors [AH06] and divisorial polytopes [IS11] which are useful for studying varieties with torus action. Se”