8 citations · 23 across the 5 of their papers we have counts for
15 papers
Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
Chien-Hao Liu, Shing-Tung Yau
We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent develop…
Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW invariants of pairs
Chien-Hao Liu, Shing-Tung Yau
The study of open/closed string duality and large duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an ope…
A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
Chien-Hao Liu, Shing-Tung Yau
In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form that arises…
-fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram
Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau
In [L-L-Y1, III: Sec. 5.4] on mirror principle, a method was developed to compute the integral for a flag manifold $X=\Fl_{r_1, ...…
On A-twisted moduli stack for curves from Witten's gauged linear sigma models
Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau
Witten's gauged linear sigma model [Wi1] is one of the universal frameworks or structures that lie behind stringy dualities. Its A-twisted moduli space at genus 0 case has been use…
The fixed points in Quot-schemes and mirror principle computations
Bong H. Lian, Chien-Hao Liu, Kefeng Liu +1
We describe the -action on the Quot-scheme $\Quot({\cal E}^n)$ associated to the trivial bundle ${\cal E}^n=CP^1\times{\smallBbb C}^n$. In particlular, the topology of the $S^…