Cheng-Yong Du
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View article: Double ramification cycles with orbifold targets
Double ramification cycles with orbifold targets Open
In this paper, we consider double ramification cycles with orbifold targets. An explicit formula for double ramification cycles with orbifold targets, which is parallel to and generalizes the one known for the smooth case, is provided. Som…
View article: On the Mare\v{s} cores of fuzzy vectors
On the Mare\v{s} cores of fuzzy vectors Open
It is known that every fuzzy number has a unique Mares core and can be decomposed in a unique way as the sum of a skew fuzzy number, given by its Mares core, and a symmetric fuzzy number. The aim of this paper is to provide a negative answ…
View article: Fuzzy vectors via convex bodies
Fuzzy vectors via convex bodies Open
In the most accessible terms this paper presents a convex-geometric approach to the study of fuzzy vectors. Motivated by several key results from the theory of convex bodies, we establish a representation theorem of fuzzy vectors through s…
View article: On fibrations of Lie groupoids
On fibrations of Lie groupoids Open
As groupoids generalize groups, motivated by group extensions we consider a kind of fibrations of Lie groupoids, called locally topological product Lie groupoid fibrations with fiber $\sf A$, i.e., \[ 1\rightarrow {\sf A} \rightarrow {\sf …
View article: Equivariant commutative stringy cohomology rings on almost complex manifolds
Equivariant commutative stringy cohomology rings on almost complex manifolds Open
In this paper, motivated by Chen--Ruan's stringy orbifold theory on almost complex orbifolds, we construct a new cohomology ring $\mathscr H^\ast_{G,cs}(X)$ for an equivariant almost complex pair $(X,G)$, where $X$ is a compact connected a…
View article: Equivariant commutative stringy cohomology rings on almost complex\n manifolds
Equivariant commutative stringy cohomology rings on almost complex\n manifolds Open
In this paper, motivated by Chen--Ruan's stringy orbifold theory on almost\ncomplex orbifolds, we construct a new cohomology ring $\\mathscr\nH^\\ast_{G,cs}(X)$ for an equivariant almost complex pair $(X,G)$, where $X$ is\na compact connec…
View article: Groupoid of morphisms of groupoids
Groupoid of morphisms of groupoids Open
In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equi…
View article: Weighted blowup correspondence of orbifold Gromov--Witten invariants and applications
Weighted blowup correspondence of orbifold Gromov--Witten invariants and applications Open
Let $\sf X$ be a symplectic orbifold groupoid with $\sf S$ being a symplectic sub-orbifold groupoid, and $\sf X_{\mathfrak a}$ be the weight-$\mathfrak a$ blowup of $\sf X$ along $\sf S$ with $\sf Z$ being the corresponding exceptional div…
View article: Spark complexes on good effective orbifold atlases categorically
Spark complexes on good effective orbifold atlases categorically Open
Good atlases are defined for effective orbifolds, and a spark complex is constructed on each good atlas. It is proved that this process is 2-functorial with compatible systems playing as morphisms between good atlases, and that the spark c…
View article: Weighted blow-up of Gromov-Witten invariants of orbifold\\ Riemannian surfaces along smooth points
Weighted blow-up of Gromov-Witten invariants of orbifold\\ Riemannian surfaces along smooth points Open
第一个公式表明, 当 (X, ω) 是辛一致规则的 (uniruled) 时, 它的沿光滑点的加权涨开 ( X, ω) 也是辛一 致规则的.关键词 轨形 Riemann 面 轨形 Gromov-Witten 不变量 加权涨开公式 辛一致规则辛手术中最简单的是辛涨开.Hu [9][10][11] 最早开始研究辛流形作涨开时 GW 不变量的变化情形.在 辛流形沿着低维辛子流形作涨开时, 有一大类 GW 不变量是保持不变的.Qi [12] 和 He 等 [13] 推广了 文献 […
View article: Ruan cohomologies of the compactifications of resolved orbifold conifolds
Ruan cohomologies of the compactifications of resolved orbifold conifolds Open
In this paper, we study the Ruan cohomologies of $X^s$ and $X^{sf}$, the natural compactifications of $V^s$ and $V^{sf}$, where $V^s$ and $V^{sf}$ are the two small resolutions of \\[ V=\\{(x,y,z,w)\\mid xy-zw=0\\}/\\mu _r(1,-1,0,0),\\quad…