2011/11/21 by Chien‐Hao Liu, Chien-Hao Liu, Shing-Tung Yau +3
Mathematics · Physics and Astronomy · #14A22 #14E15 #81T30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG #msc:14A22 #msc:14E15 #msc:81T30
paper · pdf · doi:10.48550/arxiv.1111.4707
9+2 pages
arxiv created 2011/11/21 · openalex publication_date 2011/11/21 · arxiv updated 2011/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on examples from superstring/D-brane theory since the work of Douglas and Moore on resolution of singularities of a superstring target-space Y via a D-brane probe, the richness and the complexity of the stack of punctual D0-branes on a variety, and as a guiding question, we lay down a conjecture that any resolution Y′→ Y of a variety Y over \Bbb C can be factored through an embedding of Y′ into the stack \frak M^0A zf pr (Y) of punctual D0-branes of rank r on Y for r≥ r0 in \Bbb N, where r0 depends on the germ of singularities of Y. We prove that this conjecture holds for the resolution ρ: C′→ C of a reduced singular curve C over \Bbb C. In string-theoretical language, this says that the resolution C′ of a singular curve C always arises from an appropriate D0-brane aggregation on C and that the rank of the Chan-Paton module of the D0-branes involved can be chosen to be arbitrarily large.