Stringy orbifolds
英文摘要:
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Yongbin Ruan
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
In this paper we present a model to calculate the stringy product on twisted orbifold K-theory of Adem-Ruan-Zhang for abelian complex orbifolds. In the first part we consider the non-twisted case on an orbifold presented as the quotient of a manifold acted by a compact abelian Lie group. We give an explicit description of the obstruction bundle, we explain the relation with the product defined by Jarvis-Kaufmann-Kimura and, via a Chern character map, with the Chen-Ruan cohomology, and we explicitely calculate the stringy product for a weighted projective orbifold. In the second part we conside…
For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natura…
In this note, we reconcile two approaches that have been used to construct stringy multiplications. The pushing forward after pulling back that has been used to give a global stringy extension of the functors K_0,K^{top},A^*,H^* [CR, FG, AGV, JKK2], and the pulling back after having pushed forward, which we have previously used in our (re)-construction program for G-Frobenius algebras, notably in considerations of singularities with symmetries and for symmetric products. A similar approach was also used by [CH] in their considerations of the Chen-Ruan product in a deRham setting for Abelian or…
In 1985, physicists Dixon, Harvey, Vafa and Witten studied string theories on Calabi-Yau orbifolds (cf. [DHVW]). An interesting discovery in their paper was the prediction that a certain physicist's Euler number of the orbifold must be equal to the Euler number of any of its crepant resolutions. This was soon related to the so called McKay correspondence in mathematics (cf. [McK]). Later developments include stringy Hodge numbers (cf. [Z], [BD]), mirror symmetry of Calabi-Yau orbifolds (cf. [Ro]), and most recently the Gromov-Witten invariants of symplectic orbifolds (cf. [CR1-2]). One common …
This paper exposes the fundamental role that the Drinfel'd double $\dkg$ of the group ring of a finite group $G$ and its twists $\dbkg$, $β\in Z^3(G,\uk)$ as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of $\dkg$--modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold $K$--theory of glob…
Stringy Irregular Hodge Numbers for Non-Simplicial Toric Landau--Ginzburg Data
将轨道折叠不规则Hodge理论推广至非单纯环带数据,构造滤过Koszul--de Rham复形,证明其射影crepant单纯细分模型共享同一Hodge多项式,从而定义弦论不规则Hodge数。
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