Chien‐Hao Liu

1. A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
   2004/08/11 by Chien-Hao Liu, Chien‐Hao Liu, Shing-Tung Yau +3 · 1 citation
   Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #hep-th #math.AG #msc:14N35 #msc:81T30
2. D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
   2010/03/05 by Chien‐Hao Liu, Shing–Tung Yau, Liu, Chien-Hao +1 · 4 citations
   Mathematics · Physics and Astronomy · #14A22 #53C38 #81T30 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
3. On the Global Structure of Some Natural Fibrations of Joyce Manifolds
   1998/09/01 by Chien‐Hao Liu, Chien-Hao Liu, Liu, Chien-Hao · 1 citation
   Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG #math.GT