Chien‐Hao Liu

activity

19962008

most citedAzumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint

21 citations · 63 across the 7 of their papers we have counts for

collaborators

Showing 2004Show all

3 papers · 1 filter

math.AG2004

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 $N$ duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an ope…

math.AG2004★ 6 cited

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 $Y_{1} \cup_{D} Y_{2}$ that arises…

math.AG2004★ 6 cited

$S^{1}$ -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 $\int_{X} τ^{*} e^{H \cdot t} \cap 1_{d}$ for a flag manifold $X=\Fl_{r_1, ...…

Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW invariants of pairs

A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups

S1-fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram

$S^{1}$ -fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram