相关论文: On canonical modules of toric face rings

We prove that the automorphism group of a toric Deligne-Mumford stack is isomorphic to the $2$-group associated to the stacky fan.

Our main result states that for a toric surface in $P^4$ canonical module is always Cohen-Macaulay.

Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…

I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…

Let G be a split reductive group. We introduce the moduli problem of "bundle chains" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its…

We show that the algebraic invariants multiplicity and depth of a graded ideal in the polynomial ring are closely connected to the fan structure of its generic tropical variety in the constant coefficient case. Generically the multiplicity…

Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact…

We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject to two…

The notion of a toric origami manifold, which weakens the notion of a symplectic toric manifold, was introduced by Cannas da Silva-Guillemin-Pires \cite{ca-gu-pi11} and they show that toric origami manifolds bijectively correspond to…

A new class of full fans in an euclidean space - tight fans - is introduced. Such fans are defined using a property of local symmetry in a face of a tiling. Tight fans are related to the theory of parallelotopes in an euclidean space. A…

We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for…

The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is `nonsingular', i.e., has the homology of a wedge of spheres of the…

This paper concerns homological mirror symmetry for the pair-of-pants surface (A-side) and the non-isolated surface singularity $xyz=0$ (B-side). Burban-Drozd classified indecomposable maximal Cohen-Macaulay modules on the B-side. We prove…

This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the…

After surveying higher K-theory of toric varieties, we present Totaro's old (c. 1997) unpublished result on expressing the corresponding homotopy theory via singular cohomology. It is a higher analog of the rational Chern character…

We show that under certain conditions the flyping operation on rational tangles, which produces topologically isotopic tangles, may also produce tangles which are not Legendrian isotopic when viewed in the standard contact structure on…

The main result of this paper is that every (separated) toric variety which has a semigroup structure compatible with multiplication on the underlying torus is necessarily affine. In the course of proving this statement, we also give a…

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…

The category of (abstract) fans is to the category of monoids what the category of schemes is to the category of rings: a fan is obtained by gluing spectra of monoids along open embeddings. Here we study the basic algebraic geometry of…

A toric amplitude is a rational function associated to a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their…