Linked Hom spaces (Q2428795)

Let \(F_1, \dots, F_n\) and \(G_1, \dots, G_n\) be two chains of vector bundles on a base scheme \(S\), of rank \(r\) and \(m\) respectively. Consider homomorphisms \(f_i:F_i \to F_{i+1}\), \(f^{i}:F_{i+1} \to F_i\), \(g_i:G_i \to G_{i+1}\), \(g^{i}:G_{i+1} \to G_i\). In this paper (see Def. 2.3) natural conditions on the previous data are proposed so that the linked Hom functor parameterizing tuples of morphisms \(\varphi_i:F_i \to G_i\) commuting with all the \(f\)'s and \(g\)'s is well behaved. In particular see (Thm. 1.1) it is represented by a vector bundle \(LH\) on \(S\) of rank \(rm\). This is applied to present a new version of a construction of limit linear series spaces out of linked Grassmannians by the same author (see proper references in the Bibliography of the paper under review).