Interior Estimates for the $n$-dimensional Abreu's Equation
We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.
math.DG↗
arXiv subjects
Bohui Chen
Publications and source records attributed to Bohui Chen.
Uniform K-stability for extremal metrics on toric varieties
In this paper we prove that for toric varieties the uniform K-stability is the necessary condition for the existence of extremal metrics.
math.DG↗
Interior regularity on the Abreu equation
In this paper we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the $C^0$ estimate.
math.DG↗
Relative orbifold Gromov-Witten theory and degeneration formula
Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.
math.SG↗
The Kahler Metrics of constant scalar curvature on the Complex Torus
We study the Dirichlet problem of the Abreu equation. The solutions provide the Kahler metrics of constant scalar curvature on the complex torus.
math.DG↗
Ruan's Conjecture on Singular symplectic flops
We prove that the orbifold quantum ring is preserved under singular symplectic flops. Hence we verify Ruan's conjecture for this case.
math.AG↗
Singular symplectic flops and Ruan cohomology
In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/μ_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let $X$ and $Y$ be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of exceptional classes on $X$ and $Y$ and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.
math.SG↗
A deRham model for Chen-Ruan cohomology ring of abelian orbifolds
We present a deRham model for Chen-Ruan cohomology ring of abelian orbifolds. We introduce the notion of \emph{twist factors} so that formally the stringy cohomology ring can be defined without going through pseudo-holomorphic orbifold curves. Thus our model can be viewed as the classical description of Chen-Ruan cohomology for abelian orbifolds. The model simplifies computation of Chen-Ruan cohomology ring. Using our model, we give a version of wall crossing formula.
math.SG↗
Virtual Manifolds and Localization
In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration theory. In particular, the virtual localization formula is obtained.
math.GT↗
Symplectic virtual localization of Gromov-Witten invariants
We show that moduli spaces of stable maps admits virtual orbifold structure. The symplectic version of virtual localization formula is obtained.
math.DG↗
A Smooth Compactification of the Moduli Space of Instantons and Its Application
A smooth compactification of Donaldson moduli spaces is given. As an application, we use this new space to study the wall-crossing formula and prove the Kotschick-Morgan conjecture.
math.GT↗