For (X,L) a polarized toric variety and G a torus of automorphisms of (X,L), denote by Y the GIT quotient X/G. We define a family of fully faithful functors from the category of torus equivariant reflexive sheaves on Y to the category of torus equivariant reflexive sheaves on X. We show, under a genericity assumption o…
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11 results for “torus-equivariant”
We consider a compact connected CR manifold with a transversal CR locally free -action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish -equivariant K…
Let X be a compact toric surface. There exists a sequence of torus equivariant blow-ups of X such that the blown-up toric surface obtained admits a cscK metric.
In this note we prove that toric Kähler metrics on complex projective space which are also -invariant are determined by their equivariant spectrum i.e. the list of eigenvalues of the Laplacian together with weights of the torus representation on the eigenspaces.
It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant…
Characterizes K-semistability for log Fano cone singularities.
problem K-semistability of log Fano cone singularities.
method Non-Archimedean characterization and special test configurations.
result K-semistability agrees with Collins--Székelyhidi's definition.
Generalizes Delzant theorem for torus-equivariantly embedded toric hypersurfaces.
problem Conditions for nonsingularity of complex subtorus orbits in symplectic toric manifolds.
method Clarification of Delzant theorem conditions using polytopes.
result Generalization of Delzant theorem for torus-equivariantly embedded toric hypersurfaces.
Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associated -actions. We show that there actually holds the moment convergence of the weight distributions. Our analytic approach at th…
We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity should be reduced with respect to the group action. About this point we explain …
New submanifolds found in toric manifolds with specific actions.
problem Understanding submanifolds in toric manifolds with complex subtorus actions.
method Analyzing the closure of a complex subtorus in a toric manifold and its Hamiltonian action.
result The image of the moment map for the Hamiltonian subtorus action coincides with the image of the Delzant polytope.
Logarithmic connections on principal bundles over normal varieties are studied.
problem Existence and properties of logarithmic connections on principal bundles over normal varieties.
method Introducing logarithmic connections, showing equivalence to covariant derivatives, and proving existence conditions.
result Existence of logarithmic connections on principal bundles over normal varieties is equivalent to certain conditions on the associated vector bundles and adjoint bundles.