6 papers
Moment maps, symplectomorphism groups and compatible complex structures
Miguel Abreu, Gustavo Granja, Nitu Kitchloo
In this paper we apply Donaldson's general moment map framework for the action of a symplectomorphism group on the corresponding space of compatible (almost) complex structures to…
Kahler metrics on toric orbifolds
Miguel Abreu
A theorem of E.Lerman and S.Tolman, generalizing a result of T.Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a pos…
Kahler geometry of toric manifolds in symplectic coordinates
Miguel Abreu
A theorem of Delzant states that any symplectic manifold $(M,\om)$ of dimension , equipped with an effective Hamiltonian action of the standard -torus $\T^n = \R^{n}/2π\Z^n$…
Topology of symplectomorphism groups of rational ruled surfaces
Miguel Abreu, Dusa McDuff
Let be either or the one point blow-up $\cp# \bcp$ of $\cp$. In both cases carries a family of symplectic forms $\om_\la$, where $\la > -1$ determines the c…
On the invariant spectrum of -invariant metrics on
Miguel Abreu, Pedro Freitas
A theorem of J. Hersch (1970) states that for any smooth metric on , with total area equal to , the first nonzero eigenvalue of the Laplace operator acting on functions is…
Kahler geometry of toric varieties and extremal metrics
Miguel Abreu
Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler metrics on (symplectic) toric varieties, using only data on the moment polytope. In this paper,…