Ruan’s Conjecture and Integral Structures in Quantum Cohomology
نویسنده
چکیده
This is an expository article on the recent studies [23, 24, 44, 19] of Ruan’s crepant resolution/flop conjecture [59, 60] and its possible relations to the K-theory integral structure [44, 50] in quantum cohomology.
منابع مشابه
An Integral Structure in Quantum Cohomology and Mirror Symmetry for Toric Orbifolds
We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the b Γ-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a ro...
متن کاملOrbifold Cohomology of ADE-singularities
We study Ruan’s cohomological crepant resolution conjecture [39] for orbifolds with transversal ADE singularities. In the An-case we compute both the orbifold cohomology ring H ∗ orb([Y ]) and the quantum corrected cohomology ring H(Z)(q1, ..., qn). The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between H orb([Y ])...
متن کاملHodge Structures for Orbifold Cohomology
We construct a polarized Hodge structure on the primitive part of Chen and Ruan’s orbifold cohomology Hk orb(X) for projective SL-orbifolds X satisfying a “Hard Lefschetz Condition”. Furthermore, the total cohomology ⊕ p,q H p,q orb(X) forms a mixed Hodge structure that is polarized by every element of the Kähler cone of X. Using results of Cattani-Kaplan-Schmid this implies the existence of an...
متن کاملOrbifold Cohomology of the Symmetric Product
Chen and Ruan’s orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) H∗ orb (Xn/Sn; C) ∼= H∗(X ; C) between the orbifold cohomology of the symmetric product of a smooth projective surface with trivial canonical class X and the cohomology of its Hilbert scheme X [n] is obtained, yielding a positive answer to a conject...
متن کاملOn the Crepant Resolution Conjecture in the Local Case
In this paper we analyze four examples of birational transformations between local Calabi– Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov–Witten invariants, proving the Coates–Corti–Iritani– Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008