Abstract
Let k be an algebraically closed field of characteristic zero and let A be a finitely generated k−algebra. The Nori Hilbert scheme of A, HilbnA, parameterizes left ideals of codimension n in A, and it is well known that HilbnA is smooth when A is formally smooth. In this paper we will study HilbnA for 2−Calabi Yau algebras. The main examples of these are surface group algebras and preprojective algebras. For the former we show that the Nori-Hilbert scheme is smooth for n = 1 only, while for the latter we show that the smooth components of HilbnA that contain simple representations are precisely those that only contain simple representation. Under certain conditions we can generalize this last statement to arbitrary 2−Calabi Yau algebras. Mathematics Subject Classification (2010): 14C05, 14A22, 16G20, 16E40.
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