Related papers: Towards transverse toric geometry
We develop a theory of multi-stage degenerations of toric varieties over finite rank valuation rings, extending the Mumford--Gubler theory in rank one. Such degenerations are constructed from fan-like structures over totally ordered abelian…
The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…
We introduce the category of {\it locally $k$-standard $T$-manifolds} which includes well-known classes of manifolds such as toric and quasitoric manifolds, good contact toric manifolds and moment-angle manifolds. They are smooth manifolds…
We give a complete classification of the torus-equivariant birational equivalence classes of smooth proper toric Deligne-Mumford stacks with trivial generic stabilizer in terms of their associated stacky fans.
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…
We propose new definitions of integral, reduced, and normal superrings and superschemes to properly establish the notion of a supervariety. We generalize several results about classical reduced rings and varieties to the supergeometric…
A covariant functor from the category of generic complex algebraic curves to a category of the AF-algebras is constructed. The construction is based on a representation of the Teichmueller space of a curve by the measured foliations due to…
We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…
Multi-fan is an analogous notion of fan. As a fan is associated to a toric variety a multi-fan is associated to a torus orbifold. Orbifold elliptic class and orbifold elliptic genus are defined for a triple of a multi-fan, a set of…
In this paper, we prove that there exists an equivalence between 2-category of smooth Deligne-Mumford stacks with torus-embeddings and actions, and the 1-category of stacky fans. For this purpose, we obtain two main results. The first is to…
Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset $\mathcal{A}$ of $\mathbb{Z}^n$. They may also be…
We continue the approach toward a purely combinatorial "virtual" intersection cohomology for possibly non-rational fans, based on our investigation of equivariant intersection cohomology for toric varieties (see math.AG/9904159).…
Viewing a fan as a partially ordered set (of cones) we consider a category of sheaves on the fan which corresponds to a category of equivariant sheaves on the corresponding toric variety if the fan is rational. In this category we define an…
We study the action of the dihedral group on the (equivariant) cohomology of the toric manifolds associated with cycle graphs.
In this present paper we study geometry of compact complex manifolds equipped with a \emph{maximal} torus $T=(S^1)^k$ action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan $\Sigma$ and a…
Let $\Gamma$ be a finite group acting linearly on a vector space $V$. We compute the Lie algebra cohomology of the Lie algebra of $\Gamma$-invariant formal vector fields on $V$. We use this computation to define characteristic classes for…
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin…
We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.
Real toric manifolds are the real loci of nonsingular complete toric varieties. In this paper, we calculate the integral cohomology groups of real toric manifolds in terms of the combinatorial data contained in the underlying simplicial…