[PDF] Top 20 Invariance of quantum rings under ordinary flops: III

... 2014 UNDER ORDINARY FLOPS: III YUAN-PIN LEE, HUI-WEN LIN, FENG QU, AND CHIN-LUNG WANG A BSTRACT ...part of our project to study a case of Crepant Transformation Conjecture: ... See full document

... 2013 UNDER ORDINARY FLOPS: I YUAN-PIN LEE, HUI-WEN LIN, AND CHIN-LUNG WANG A BSTRACT ...first of a sequence of papers proving the quan- tum invariance under ... See full document

... comparisons of J-functions and Birkhoff factorizations on X and X ′ ...regularization of certain rational functions leads to the begin- ning steps of analytic continuations in our ... See full document

... vanishing of GW invariants of extremal rays follows from the previous ...Instead of using deformation invariance of relative GW the- ory, we may also proceed in the same way as the case ... See full document

... the invariance of big quantum products, nonextremal curve classes need to be ...purpose of Section 4 is to reduce the case of general X to the local ...terms of relative ... See full document

... definition of flops, we get ( ...case of ordinary Mukai flop, i.e. k = 1. Remark 4.4. For A n,2 flops, the deformed flop F t is a family of ordinary flop, which has defect ... See full document

... study of invariance of quantum product under ordinary flops in higher dimensions was started in ...the quantum invariance under F = T ∗ : QH ( X ) → ... See full document

... type of flops and also crucial to the general theory of minimal models and K-equivalence, so it is natural to work on them ...sense of minimal model theory, with ¯ ψ : Z → S the restriction map on the ... See full document

... Statement of the main ...sense of minimal model theory, with c : Z G P r ! pt the restriction map to the extremal ...X of X and ^ X X 0 of X 0 . Furthermore, the big quantum cohomology ... See full document

... the invariance of quantum coho- mology and Gromov-Witten theory under flop transitions up to analytic continu- ations over the extended K¨ahler ...case of ordinary flops ... See full document

... There is a sub-degeneration of VHS which corresponds the the vanishing cycle along π, whose Picard-Fuchs equation turns out have f (a) as its solution, up to a mirror change of variable![r] ... See full document

... coefficient of z − 1 in J = ...defect of cup product implies F I X 6= I X 0 and the comparison via tracking the defects of ring isomorphism becomes hopelessly ...ring of differential operators ... See full document

... They preserve all interesting in- variants like diffeomorphism type, Hodge type (Chow motive via [Y ]+[ E ]) and quantum rings etc. In fact all quantum corrections are zero..[r] ... See full document

... GLUEING QUANTUM D MODULES OVER FLOPS CHIN-LUNG WANG A BSTRACT ...theorem of two quantum D modules QH ( X ) and QH ( X 0 ) via analytic continuations over the K¨ahler moduli, where X and X 0 ... See full document

... Conclusion: I We still don’t know how to connect two Calabi–Yau 3-folds of different topological types through extremal transitions. I If there is indeed an extremal transition Y & X, then it is reasonable to ... See full document

... the invariance in higher genus, up to analytic continuation, from our results [12] in genus ...semi-simple quantum co- homology, and we trace the effect of analytic continuation carefully during the ... See full document

... principle of path integral, correlation can be calculated as weighted integral among all possible paths (world sheets) of ...weight of each path is determined by an action ... See full document

... presentence of As atoms during the post-soaking procedure. 12 Similar quantum- ring (QR) structures formed after GaAs capping layer growth are also observed in ...exchange of the buried Gasb QDs with ... See full document

... symmetrical quantum rings for both single particles and for excitons has been discovered in ...properties of In c Ga 1−c /GaAs semicon- ductor self-assembled quantum rings (SAQRs) ... See full document

... solutions of a free electron in a quantum ring to be a set of basis to solve the problem of a concentric quantum double ring with one finite potential barrier in the middle of ... See full document