Related papers: The Orbifold Cohomology Ring of Simplicial Toric S…

We show that a toroidal morphism can be reduced to a weakly semistable one in a universal way if we allow families to be modified to Deligne-Mumford stacks instead of schemes.

We extend work of Davis and Januszkiewicz by considering {\it omnioriented} toric manifolds, whose canonical codimension-2 submanifolds are independently oriented. We show that each omniorientation induces a canonical stably complex…

For $n\leq 6$, we compute the integral Chow ring of every modular compactification of $\mathcal{M}_{1,n}$ parametrising only Gorenstein curves with smooth, distinct markings. These include the Deligne--Mumford, Schubert, and Smyth…

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original…

We construct, using geometric invariant theory, a quasi-projective Deligne-Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded A-infinity-algebras. The tangent…

Comparing to the Chen-Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods…

We determine the Chow ring of the stack of truncated displays and more generally the Chow ring of the stack of G-zips. We also investigate the pull-back morphism of the truncated display functor. From this we can determine the Chow ring of…

These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for…

We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to…

We define the tautological ring as the subring of the Chow ring of a Shimura variety generated by all Chern classes of all automorphic bundles. We explain its structure for the special fiber of a good reduction of a Shimura variety of Hodge…

This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative…

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$…

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable…

Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T^k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their…

We determine the integral Chow and cohomology rings of the moduli stack $\mathcal{B}_{r,d}$ of rank $r$, degree $d$ vector bundles on $\mathbb{P}^1$ bundles. We first show that the rational Chow ring $A_{\mathbb{Q}}^*(\mathcal{B}_{r,d})$ is…

This paper is the first in a series of four papers aiming to describe the (almost integral) Chow ring of $\bar{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we introduce the moduli stack…

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be…

We give a Klyachko-type classification of topological/smooth/holomorphic $(\mathbb{C}^{*})^n$-equivariant vector bundles that are equivariantly trivial over invariant affine charts. This generalizes Klyachko's classification of toric vector…

The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with coefficients in representations" and a Chern character, and we prove a…

We define Reichstein transforms to be certain birational transformations of Artin stacks with good moduli spaces. Our main technical result is that the Reichstein transform of an Artin toric stack is again an Artin toric stack. This leads…