154 research outputs found
Toric topology
We survey some results on toric topology.Comment: English translation of the Japanese article which appeared in
"Sugaku" vol. 62 (2010), 386-41
All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions
For Gorenstein quotient spaces , a direct generalization of the
classical McKay correspondence in dimensions would primarily demand
the existence of projective, crepant desingularizations. Since this turned out
to be not always possible, Reid asked about special classes of such quotient
spaces which would satisfy the above property. We prove that the underlying
spaces of all Gorenstein abelian quotient singularities, which are embeddable
as complete intersections of hypersurfaces in an affine space, have
torus-equivariant projective crepant resolutions in all dimensions. We use
techniques from toric and discrete geometry.Comment: revised version of MPI-preprint 97/4, 35 pages, 13 figures,
latex2e-file (preprint.tex), macro packages and eps-file
Subword complexes, cluster complexes, and generalized multi-associahedra
In this paper, we use subword complexes to provide a uniform approach to
finite type cluster complexes and multi-associahedra. We introduce, for any
finite Coxeter group and any nonnegative integer k, a spherical subword complex
called multi-cluster complex. For k=1, we show that this subword complex is
isomorphic to the cluster complex of the given type. We show that multi-cluster
complexes of types A and B coincide with known simplicial complexes, namely
with the simplicial complexes of multi-triangulations and centrally symmetric
multi-triangulations respectively. Furthermore, we show that the multi-cluster
complex is universal in the sense that every spherical subword complex can be
realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio
- …