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.
Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
We established a relation between elliptic Gromov-Witten invariants of a symplectic man-ifold M and its blowups along smooth curves and surfaces.
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 coho-mology 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.… (More)