22 citations · 221 across the 45 of their papers we have counts for
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Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes
Chien-Hao Liu
In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of…
D0-brane realizations of the resolution of a reduced singular curve
Chien-Hao Liu, Shing-Tung Yau
Based on examples from superstring/D-brane theory since the work of Douglas and Moore on resolution of singularities of a superstring target-space via a D-brane probe, the rich…
Immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and its deviation from Joyce's criteria: Potential image-support rigidity of A-branes that wrap around a sL
Chien-Hao Liu, Shing-Tung Yau
Using a hyperKähler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural f…
Algebraic cobordism of filtered vector bundles on varieties: Notes on a work of Lee and Pandharipande
Chien-Hao Liu, Yu-jong Tzeng, Shing-Tung Yau
The construction of double point cobordism groups of vector bundles on varieties in the work [Lee-P] (arXiv:1002.1500 [math.AG]) of Yuan-Pin Lee and Rahul Pandharipande gives immed…