On quiver Grassmannians and orbit closures for gen-finite modules (Q2118269)

Suppose \(A=KQ/I\) is a finite dimensional basic algebra over a field \(K\). An \(A\)-module \(M\) is said to be gen-finite provided the category \(\mathrm{gen}(M)\), consisting of quotient modules of finite direct sums of copies of \(M\), has finitely many indecomposable objects up to isomorphism. The authors show that endomorphism rings of cogenerators in the module category of \(A\) admit a canonical tilting module, whose tilted algebra \(B\) is related to \(A\) by a recollement. Moreover, if \(M\) is a gen-finite \(A\)-module, they construct desingularisations of the orbit closure and quiver Grassmannians of \(M\). In particular, they are able to generalize all results from [\textit{W. Crawley-Boevey} and \textit{J. Sauter}, Math. Z. 285, No. 1--2, 367--395 (2017; Zbl 1405.16028)].