Completely integrable torus actions on complex manifolds with fixed points
نویسندگان
چکیده
منابع مشابه
Completely Integrable Torus Actions on Complex Manifolds with Fixed Points
We show that if a holomorphic n-dimensional compact torus action on a compact connected complex manifold of complex dimension n has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.
متن کاملComplex structures on 4-manifolds with symplectic 2-torus actions
We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a 4-manifold with a symplectic 2-torus action admits an invariant complex structure and give an identification of those that do not admit a Kähler structure with Kodaira’s class of complex surfaces which admit a nowhere vanishing holomorphic (2, 0)-form, but are not a torus or a K3 surface.
متن کاملGkm Theory for Torus Actions with Non-isolated Fixed Points
LetM be a compact symplectic manifold and T a compact n-dimensional torus. A Hamiltonian action, τ , of T on M is a GKM action if, for every p ∈ M , the isotropy representation of T on TpM has pair-wise linearly independent weights. For such an action the projection of the set of zero and one-dimensional orbits onto M/T is a regular dvalent graph; and Goresky, Kottwitz and MacPherson have prove...
متن کاملFixed Points of Local Actions of Lie Groups on Real and Complex 2-Manifolds
I discuss old and new results on fixed points of local actions by Lie groups G on real and complex 2-manifolds, and zero sets of Lie algebras of vector fields. Results of E. Lima, J. Plante and C. Bonatti are reviewed.
متن کاملTORUS AND Z/p ACTIONS ON MANIFOLDS
Let G be either a finite cyclic group of prime order or S. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M , then each term of the Leray spectral sequence of the map M×GEG → BG satisfies a properly defined “Poincaré duality.” As a consequence of this fact we obtain new results relating the cohomology groups of M and M. We apply our results to study group a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2012
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2012.v19.n6.a9