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

... 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

... invariants of a P 1 bundle with those of its base, without invoking fiberwise ...deformation invariance of F -invariance is established in Section ... 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

... α i X g,n,β = h Fα i X g,n,Fβ 0 for any g, n, β including descendent ...vanishing of GW invariants of extremal rays follows from the previous ...Instead of using deformation ... 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

... 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

... definition of flops, we get ( ...case of ordinary Mukai flop, ...n,2 flops, the deformed flop F t is a family of ordinary flop, which has defect of cup product by ... See full document

... coefficient of z − 1 in J = ...the I- functions. One might be tempted to prove the F -invariance by comparing I X and I X 0 ...defect of cup product implies F I X 6= ... See full document

... UNDER ORDINARY FLOPS CHIN-LUNG WANG A BSTRACT . For ordinary flops over a smooth base, we determine the de- fect of cup product under the canonical correspondence and show ... See full document

... non-uniqueness of minimal models in higher dimensional birational geometry, ...notion of K-equivalent varieties to generalize bira- tional minimal models ... 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

... 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

... study flops first. A major one is that flops preserve cohomology groups (the number of ...the quantum effects split per- fectly into A model and B model respectively and we are led to claim ... See full document

... 0. I NTRODUCTION 0.1. Statement of the main ...sense of min- ¯ imal model theory, with ¯ ψ : Z ∼ = P r → pt the restriction map to the ex- tremal ...X of X and ˆ X 0 of X 0 . ... See full document

... • Later in April, we overcame the technical details to reduce the general case to local models, hence completely solved the invariance of QH under simple flops in all dimensions. • This is one ... See full document

... GLUEING QUANTUM D MODULES OVER FLOPS CHIN-LUNG WANG A BSTRACT ...note I summarize my talk at Sanya on December 19, ...theorem of two quantum D modules QH ( X ) and QH ( X 0 ) via ... 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 ... 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