The role of the Ellingsrud-Strømme construction in the classification of instantons (Q2392875)

A rank 2 instanton is a vector bundle of rank 2 on \(\mathbb{P}^3\) with \(H^0(E)=H^1(E(-2))=0\), \(c_1(E)=0, c_2(E)=n=\dim H^0(E(-1))\). There is enormous amount of work done in studying these, but many interesting questions remain. In [Math. Ann. 255, 123--135 (1981; Zbl 0438.14009)], \textit{G. Ellingsrud} and \textit{S. A. Strømme} studied instantons in the special case of \(c_2=3\). The authors connect their construction and a different construction of \textit{A. N. Tyurin} [Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. II: Geometry, Prog. Math. 36, 433--450 (1983; Zbl 0541.14013)] and explore the next case of \(c_2=4\).