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Journals and Conferences
In this paper, usng the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.
There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study… (More)
Over the last few years, many mathematicians contributed their efforts to establish the mathematical foundation of the theory of quantum cohomology or Gromov-Witten (GW) invariants. In 1995, Ruan and Tian [13, 15] first established for the semipositive symplectic manifolds. Recently, the semipositivity condition has been removed by many authors. Now, the… (More)
This paper obtained the switching impulse flashover characteristic of live working complex gap on extra high voltage (EHV) and ultra high voltage (UHV) high-voltage transmission lines by a large number of experiments. Based on the experimental data and the leader inception discharge model, the complex gap discharge development during the process of entering… (More)
Suppose that two compact manifolds X,X ′ are connected by a sequence of Mukai flops. In this paper, we construct a ring isomorphism between cohomology ring of X and X ′. Using the localization technique, we prove that the quantum corrected products on X,X ′ are the ordinary intersection products. Furthermore, X,X ′ have isomorphic Ruan cohomology. i.e. we… (More)