2004/08/02 by Igor Frenkel, Frenkel, Igor, Marcos Jardim +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Instanton #Mathematical physics #Mathematics #Minkowski space #Moduli space #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.math/0408027
57 pages, sequel to math.AG/0205118
arxiv created 2004/08/02 · openalex publication_date 2004/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use a complex version of the celebrated Atiyah-Hitchin-Drinfeld-Manin matrix equations to construct admissible torsion-free sheaves on \p3 and complex quantum instantons over our quantum Minkowski space-time. We identify the moduli spaces of various subclasses of sheaves on \p3, and prove their smoothness. We also define the Laplace equation in the quantum Minkowski space-time, study its solutions and relate them to the admissibility condition for sheaves on \p3.