On moduli spaces for quasitilted algebras.
The paper contributes to the program of characterizing classes of finite dimensional algebras -- originally defined in terms of module theory -- by geometric properties of associated algebraic varieties parametrizing modules over the algebra. An algebra \(\Lambda\) is called quasitilted if \(\Lambda\) is the endomorphism algebra of a tilting object in a connected hereditary abelian \(k\)-category with finite-dimensional homomorphism and extension spaces.NEWLINENEWLINE The main result of the paper is that every tame quasitilted algebra \(\Lambda\) satisfies the following property: for any dimension vector \(d\), for any connected component \(C\) of the variety of \(d\)-dimensional \(\Lambda\)-modules, and any weight \(\theta\) such that \(C\) contains a \(\theta\)-semistable point, the moduli space \(M(C)^{ss}_\theta\) of \(\theta\)-semistable points in \(C\) is a product of projective spaces. -- Note that together with earlier results of \textit{C. Chindris} [Algebra Number Theory 7, No. 1, 193-214 (2013; Zbl 1297.16016)] this gives a characterization of tameness for quasitilted algebras.
scientific article; zbMATH DE number 6353691