[PDF] Top 20 Quantum Invariance under Flops and Transitions

... 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

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

... of flops, we get ( ...n,2 flops, the deformed flop F t is a family of ordinary flop, which has defect of cup product by ...invariant under deformations, the fiber product of f does not pre- serve the ... See full document

... §1. Introduction To study topological problems arising from the non-uniqueness of minimal models in higher dimensional birational geometry, C.-L. Wang in 1998 raised the notion of K-equivalent varieties to generalize ... See full document

... BF/GMT and regularization 35 References 43 ...of quantum invariance of genus zero Gromov–Witten theory under flops over a non-trivial ...product under the canonical ... See full document

... 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 ) is ... 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 of the ... See full document

... 2013 UNDER ORDINARY FLOPS: I YUAN-PIN LEE, HUI-WEN LIN, AND CHIN-LUNG WANG A BSTRACT ...tum invariance under ordinary flops over a smooth ...product under the canonical ... See full document

... proof, and can be omitted in the first reading by assuming the ...recall and prove some general results about the fiber ...deformation invariance of F -invariance is established in Section ... See full document

... X and X 0 are ...deformation invariance of relative GW the- ory, we may also proceed in the same way as the case of ordinary flops, at least for simple Mukai ...invariants and then we may use ... See full document

... the invariance of big quantum products, nonextremal curve classes need to be .../ and h˛ 2 i . z E ;E / , where Y ! X is the blow-up of X over Z and z E D P Z ...ordinary flops, Y D Y 0 ... See full document

... Our result suggests that a more natural framework to study crepant transformation conjecture is to use ancestors rather than descendents. We leave the interested reader to consult [2] and references therein. 0.4. ... See full document

... Chin-Lung Wang National Taiwan University (joint with Y.-P... App-II, blow-ups (along c.i.[r] ... See full document

... modification and D modules. In principle, knowing BF, GMT and GW invariants on S allows us to calculate all g = 0 invariants on X and X 0 by ...X and I X 0 ...0 and the comparison via ... See full document

... 3 and postpone the degeneration analysis till section ...varieties and localizations had been effectively used to solve the genus zero ...the invariance in higher genus, up to analytic continuation, ... See full document

... translational invariance at the boundaries, and can be explained in terms of an effective finite single-particle interedge tunneling, which decays exponentially with increasing ...gapless and the ... See full document

... solutions under stirring. Two composites, designated as SE/CdS(1) and SE/CdS(4) depending on unsaturated and saturated CdS concentrations incorporated into SE copolymers, were cast from the DMF ...SE ... See full document

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

... The quantum theory of nonlinear effects for optical transitions of electrons in quasi-zero dimensional (Q0D) quantum dots fabricated from n-type III–V compound semiconductor materials such as n-type ... See full document