Translation quiver varieties |
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| Institution: | 1. School of Mathematics, Trinity College Dublin, Ireland;2. Hamilton Mathematics Institute, Ireland;1. Università degli Studi di Udine, Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Via delle Scienze 206, 33100 Udine, Italy;2. Università degli Studi di Firenze, Dipartimento di Matematica e Informatica, Viale Morgagni, 67/a, 50134 Firenze, Italy;3. Institut de Mathématiques, Université de Neuchâtel, Emile-Argand 11, CH-2000 Neuchâtel, Switzerland;1. Institute of Mathematics, Czech Academy of Sciences, ?itná 25, 115 67, Prague, Czech Republic;2. Tallinn University of Technology, Akadeemia tee 21b, 12618, Tallinn, Estonia;1. The Ohio State University at Lima, Lima, OH, USA;2. Università di Camerino, Camerino, Italy;1. Universidade Estadual de Campinas, IMECC, Campinas, SP, Brazil;2. Saint Petersburg State University, Russia;1. Departamento de Matemática, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil;2. Department of Mathematics, State University of Campinas, 651 Sergio Buarque de Holanda, 13083-859 Campinas, SP, Brazil |
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| Abstract: | We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under toric actions can be again realized as translation quiver varieties. This allows one to simplify quiver varieties in several steps. We prove that translation quiver varieties are smooth, pure and have Tate motivic classes. We also describe an algorithm to compute those motivic classes. |
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| Keywords: | 16G20 14N35 |
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