Algebraic classification of ℂPⁿinstanton solutions

Abstract

The finite condition for two-dimensional ℂP ⁿ models is discussed noting that one can impose boundary conditions such that the domain of the field is a compact Riemann surface S _g. Holomorphic maps φ: S _g →ℂP ⁿ give finite energy solutions of the classical field equations, which are classified according to standard methods of algebraic geometry. The moduli problem is discussed in detail for S _g =ℂP ¹=S ².