Classical solutions of \({\mathbb{C}}P^ n\) non linear \(\sigma\)-models; an algebraic geometrical description (Q1073112)

Smooth maps \(\phi\) : \(S_ g\to {\mathbb{P}}^ n\) from a surface \(S_ g\) of genus g into complex projective r-space which minimize the energy functional \(E(\phi)=\int_{S_ g}\epsilon (\phi)\quad are\) studied in order, for instance, to see if they are holomorphic. The absolute minima of this energy function are the instantons and the moduli space of such instantons in terms of linear series on \(S_ g\) is determined. Thus the interplay between algebraic geometry and mathematical physics is exposed. Although the paper is somewhat rambling, it is generally easy to read with many interesting aspects.