Complex ADHM equations, sheaves on P^3 and quantum instantons

Details Complex ADHM equations, sheaves on P^3 and quantum instantons Complex ADHM equations, sheaves on P^3 and quantum instantons

2004-08-02

arxiv.org/abs/math/0408027v1

Mathematics

Representation Theory

57 pages, sequel to math.AG/0205118

Scientific paper

We use a complex version of the celebrated Atiyah-Hitchin-Drinfeld-Manin matrix equations to construct admissible torsion-free sheaves on $\p^3$ and complex quantum instantons over our quantum Minkowski space-time. We identify the moduli spaces of various subclasses of sheaves on $\p^3$, 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 $\p^3$.

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