Actions of Cremona groups on CAT(0) cube complexes

Lonjou, Anne; Urech, Christian

doi:10.1215/00127094-2021-0061

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Theorem 22 ([27]1

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2024

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Cited by 8 publications

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“…The following proposition is a classical result (see also [17,Proposition 3.11] for a modern proof using actions on CAT(0) cubes complexes): Proposition 2.5. -Let X be a surface and G be a connected algebraic subgroup of Bir(X).…”

Section: Theorem 22 ([27]mentioning

confidence: 99%

Connected algebraic groups acting on algebraic surfaces

Pascal¹

2024

Annales De l'Institut Fourier

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Section: Theorem 22 ([27]mentioning

confidence: 99%

Connected algebraic groups acting on algebraic surfaces

Pascal¹

2024

Annales De l'Institut Fourier

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show abstract

A Metric Fixed Point Theorem and Some of Its Applications

Karlsson

2024

Geom. Funct. Anal.

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A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and compact Kähler manifolds. A special case of the fixed point theorem provides a novel mean ergodic theorem that in the Hilbert space case implies von Neumann’s theorem. The theorem accommodates classically fixed-point-free isometric maps such as those of Kakutani, Edelstein, Alspach and Prus. Moreover, from the main theorem together with some geometric arguments of independent interest, one can deduce that every bounded invertible operator of a Hilbert space admits a nontrivial invariant metric functional on the space of positive operators. This is a result in the direction of the invariant subspace problem although its full meaning is dependent on a future determination of such metric functionals.

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Families of automorphisms on abelian varieties

Favre,

Kuznetsova

2024

Math. Ann.

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Actions of Cremona groups on CAT(0) cube complexes

Cited by 8 publications

References 25 publications

Connected algebraic groups acting on algebraic surfaces

Connected algebraic groups acting on algebraic surfaces

A Metric Fixed Point Theorem and Some of Its Applications

Families of automorphisms on abelian varieties

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