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, Hilbn parameterizes left ideals of codimension n in A. It is well known that A is smooth when A is formally smooth. In this paper we will study Hilbn A for 2-Calabi-Yau algebras. Impor-tant examples include the group algebra of the fundamental group of a In this paper we will study Hilbn compact orientable surface of genus g, and preprojective algebras. For the former, we show that the Nori-Hilbert scheme is smooth only for n = 1, while for the latter we show that a component of Hilbn containing a simple representation is smooth if and only if it only contains simple representations. Under certain conditions, we generalize this last statement to arbitrary 2-Calabi-Yau algebras.

The Nori-Hilbert scheme is not smooth for 2-Calabi Yau algebras

GALLUZZI, Federica;
2016-01-01

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, Hilbn parameterizes left ideals of codimension n in A. It is well known that A is smooth when A is formally smooth. In this paper we will study Hilbn A for 2-Calabi-Yau algebras. Impor-tant examples include the group algebra of the fundamental group of a In this paper we will study Hilbn compact orientable surface of genus g, and preprojective algebras. For the former, we show that the Nori-Hilbert scheme is smooth only for n = 1, while for the latter we show that a component of Hilbn containing a simple representation is smooth if and only if it only contains simple representations. Under certain conditions, we generalize this last statement to arbitrary 2-Calabi-Yau algebras.
2016
10
2
745
774
https://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=10&iss=2&rank=11&srch=searchterm|galluzzi
Representation Theory, Calabi-Yau Algebras, Nori-Hilbert Scheme.
Raf Bocklandt; Federica Galluzzi; Francesco Vaccarino
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/151469
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