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

... 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

... 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

... 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

... 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, 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

... 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

... 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

... 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 . Furthermore, the big quantum ... 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

... instead of blue ...prediction of blue shift with reduced nano- structure ...instead of GaSb/GaAs interfaces are obtained between the GaSb QRs and GaAs ... 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

... dynamics of standard and coupled quantum rings (QRs) of type-II GaSb/GaAs are ...increase of the tempera- ture would firstly decrease and then increase the FWHM of QR PL ... See full document

... linearity of V OC under ...1.3 under higher concentration, which could be viewed as the saturation of the defect-related ...result of the same epitaxial structure and fabrication ... See full document