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Cohomology rings of moduli of point configurations on the projective line


Authors: Hans Franzen and Markus Reineke
Journal: Proc. Amer. Math. Soc. 146 (2018), 2327-2341
MSC (2010): Primary 14D22; Secondary 14N10, 16G20
DOI: https://doi.org/10.1090/proc/14024
Published electronically: March 9, 2018
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhibit such a moduli space admitting two small desingularizations with non-isomorphic cohomology rings.


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  • [1] Dan Edidin and William Graham, Equivariant intersection theory, Invent. Math. 131 (1998), no. 3, 595-634. MR 1614555
  • [2] H. Franzen, Chow rings of fine quiver moduli are tautologically presented, Math. Z. 279 (2015), no. 3-4, 1197-1223. MR 3318266
  • [3] H. Franzen and M. Reineke, Semi-stable Chow-Hall algebras of quivers and quantized Donaldson-Thomas invariants, Preprint. arXiv:1512.03748, 2015.
  • [4] M. Goresky and R. MacPherson, Problems and bibliography on intersection homology, Intersection cohomology (Bern, 1983) Progr. Math., vol. 50, Birkhäuser Boston, Boston, MA, 1984, pp. 221-233. MR 788180
  • [5] J.-C. Hausmann and A. Knutson, The cohomology ring of polygon spaces, Ann. Inst. Fourier (Grenoble) 48 (1998), no. 1, 281-321 (English, with English and French summaries). MR 1614965
  • [6] Benjamin Howard, John Millson, Andrew Snowden, and Ravi Vakil, The equations for the moduli space of $ n$ points on the line, Duke Math. J. 146 (2009), no. 2, 175-226. MR 2477759
  • [7] A. D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), no. 180, 515-530. MR 1315461
  • [8] Alastair D. King and Charles H. Walter, On Chow rings of fine moduli spaces of modules, J. Reine Angew. Math. 461 (1995), 179-187. MR 1324213
  • [9] D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994. MR 1304906
  • [10] Markus Reineke, Quiver moduli and small desingularizations of some GIT quotients, Representation theory--current trends and perspectives, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2017, pp. 613-635. MR 3644807

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Additional Information

Hans Franzen
Affiliation: Faculty of Mathematics, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany
Email: hans.franzen@rub.de

Markus Reineke
Affiliation: Faculty of Mathematics, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany
Email: markus.reineke@rub.de

DOI: https://doi.org/10.1090/proc/14024
Received by editor(s): December 9, 2016
Received by editor(s) in revised form: July 26, 2017
Published electronically: March 9, 2018
Additional Notes: This research was supported by DFG SFB/Transregio 191 “Symplektische Strukturen in Geometrie, Algebra und Dynamik”.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2018 American Mathematical Society

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