ﻻ يوجد ملخص باللغة العربية
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 on G, that slope stability is preserved by these functors if and only if the pair ((X, L), G) satisfies a combinatorial criterion. As an application, when (X,L) is a polarized toric orbifold of dimension n, we relate stable equivariant reflexive sheaves on (X, L) to stable equivariant reflexive sheaves on certain (n-1)-dimensional weighted projective spaces.
We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ing
We investigate the equivariant intersection cohomology of a toric variety. Considering the defining fan of the variety as a finite topological space with the subfans being the open sets (that corresponds to the toric topology given by the invariant o
For a given K-polystable Fano manifold X and a natural number l, we show that there exists a rational number 0 < c < 1 depending only on the dimension of X, such that $Din |-lK_X|$ is GIT-(semi/poly)stable under the action of Aut(X) if and only if th
We extend the results of [GVX] to the setting of a stable polar representation G|V (G connected, reductive over C), satisfying some mild additional hypotheses. Given a G-equivariant rank one local system L on the general fiber of the quotient map f :
We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal opt