8 citations · 18 across the 10 of their papers we have counts for
4 papers · 1 filter
Cosmic String, Harvey-Moore Conjecture and Family Seiberg-Witten Theory
Ai-Ko Liu
In this paper, we study the enumeration of virtual numbers of immersed nodal curves along certain Calabi-Yau K3 fibrations. By using the concept of cosmic strings, we verify the mo…
The Residual Intersection Formula of Type II Exceptional Curves
Ai-Ko Liu
The paper is a part of our program to build up a theory of couting immersed nodal curve on algebraic surfaces, as an enumerative Riemann-Roch theory (outlined in math.AG/0405113).…
A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem
Ai-Ko Liu
The paper is a short supplement of the longer paper "The Algebraic Proof of the Universality Theorem", preprint math.AG/0402045. In this short note, we outline the geometric meanin…
The Algebraic Proof of the Universality Theorem
Ai-Ko Liu
In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or g…