A construction of the Deligne--Mumford orbifold

Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds

We develop differential and symplectic geometry of differentiable Deligne-Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks as symplectic quotients of C^NxBG, where G is a finite non-abelian group.

Gromov-Witten theory of Deligne-Mumford stacks

Long ago, in math.AG/0112004, we pledged more details on the algebraic version of Chen-Ruan's math.AG/0103156. This is it.

Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks

We introduce a global Landau-Ginzburg model which is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-modules (and of the all-genus Gromov-Witten potentials) under a discrepant toric wall-crossing. In the case of weighted blowups of weak-Fano compact toric stacks along toric centres, we show that an analytic lift of the formal decomposition corresponds, via the $\widehatΓ$-integral structure, to an Orlov-type semiorthogonal decomposition of topologic…

Global quotients among toric Deligne-Mumford stacks

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected component $G_0$ on $M$ and is related to (stacky) fundamental group and covering theory. This characterization is then applied to smooth toric Deligne-Mumford stacks, and global quotients among toric DM stacks are then characterized in terms of their associated combinatorial data of stac…

具有共轭标记点的实有理曲线Deligne-Mumford模空间的上同调环

The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points

本文证明了具有共轭标记点的实有理曲线Deligne-Mumford模空间的有理上同调环可由复边界除子与实边界超曲面生成，并模去明显几何关系及先前识别的正维数正余维数关系。

The symplectic Deligne-Mumford stack associated to a stacky polytope

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.