8 citations · 18 across the 10 of their papers we have counts for
4 papers · 1 filter
Family Switching Formula and the Exceptional Rational Curves
Ai-Ko Liu
In this paper, we derive the family switching formula of -n two-sphere fiber bundle embedded in a smooth four-manifold fiber bundle. In the smooth category, it is a partial general…
A Note on Curve Counting Scheme in an Algebraic Family and The Admissible Decomposition Classes
Ai-Ko Liu
Mcduff had proposed in 1997 a way to modify the definition of Taubes' version of Gromov invariant when multiple coverings of -1 curves appear. In this paper we generalize Mcduff's…
The Family Blowup Formula of the Family Seiberg-Witten Invariants
Ai-Ko Liu
In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular cu…
Family Blow Up Formula, Admissible Graphs and the counting of Nodal Curves
Ai-Ko Liu
The family Blow Up formula is recalled. Certain combinatoric graphs are introduced for the discussion of the counting of nodal curves on an Kahler surface.