[PDF] Top 20 Flops, Motives and Invariance of Quantum Rings

... X and X 0 are equivalent. The statement on vanishing of GW invariants of extremal rays follows from the previous ...Instead of using deformation invariance of relative GW the- ... 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

... 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 ordinary flops over a smooth ... See full document

... proof, and can be omitted in the first reading by assuming the ...recall and prove some general results about the fiber ...invariants of a P 1 bundle with those of its base, without invoking ... 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

... Outline of the contents. In Section 2, the existence of A n,k flops in the projective category is proved via the cone ...equivalence of Chow motives via graph closure is established for ... See full document

... Statement of the main results. Let X be a smooth complex projective mani- fold and c : X ! X a flopping contraction in the sense of minimal model theory, with c : Z G P r ! pt the restriction map to ... 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

... non-uniqueness of minimal models in higher dimensional birational geometry, ...notion of K-equivalent varieties to generalize bira- tional minimal models ...X and X  are K-equivalent if there exist ... 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

... • 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

... 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 ... 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 of invariance of quantum product under ordinary flops in higher dimensions was started in ...] and the quantum invariance under F = T ∗ : QH ( X ) → QH ( X 0 ... 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

... 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 ... See full document

... Microscale and mesoscale metallic and semiconductor quantum rings have been received a considerable attention for ...fabrication of semiconductor nanostructures have allowed us to ... See full document

... made of the conditional averages of the magnetization and magnetic susceptibility of dispersive ensembles of nano-objects with a very complex geometry—self-assembled wobbled ... See full document

... Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois 60612, USA ...impact of the sizes and the shapes of nanoscale semiconductor quantum ... See full document

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