Torus-Equivariant Chow Rings of Quiver Moduli
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We compute rational equivariant Chow rings with respect to a torus of quiver moduli spaces. We derive a presentation in terms of generators and relations, use torus localization to identify it as a subring of the Chow ring of the fixed point locus, and we compare the two descriptions.
Keywords: equivariant Chow rings, torus localization
Mots-clés : torus actions, quiver moduli.
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     author = {Hans Franzen},
     title = {Torus-Equivariant {Chow} {Rings} of {Quiver} {Moduli}},
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     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a95/}
}
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Hans Franzen. Torus-Equivariant Chow Rings of Quiver Moduli. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a95/

[1] Altmann K., Hille L., “Strong exceptional sequences provided by quivers”, Algebr. Represent. Theory, 2 (1999), 1–17 | DOI | MR | Zbl

[2] Assem I., Skowroński A., Simson D., Elements of the representation theory of associative algebras, v. 1, London Mathematical Society Student Texts, 65, Techniques of representation theory, Cambridge University Press, Cambridge, 2006 | DOI | MR | Zbl

[3] Brion M., “Equivariant Chow groups for torus actions”, Transform. Groups, 2 (1997), 225–267 | DOI | MR | Zbl

[4] Chang T., Skjelbred T., “The topological Schur lemma and related results”, Ann. of Math., 100 (1974), 307–321 | DOI | MR | Zbl

[5] Edidin D., Graham W., “Equivariant intersection theory”, Invent. Math., 131 (1998), 595–634, arXiv: alg-geom/9609018 | DOI | MR

[6] Franzen H., Reineke M., “Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants”, Algebra Number Theory, 12 (2018), 1001–1025, arXiv: 1512.03748 | DOI | MR | Zbl

[7] Franzen H., Reineke M., Sabatini S., Fano quiver moduli, arXiv: 2001.10556

[8] Goresky M., Kottwitz R., MacPherson R., “Equivariant cohomology, Koszul duality, and the localization theorem”, Invent. Math., 131 (1998), 25–83 | DOI | MR | Zbl

[9] King A. D., “Moduli of representations of finite-dimensional algebras”, Quart. J. Math. Oxford Ser. (2), 45 (1994), 515–530 | DOI | MR | Zbl

[10] Kresch A., “Cycle groups for Artin stacks”, Invent. Math., 138 (1999), 495–536, arXiv: math.AG/9810166 | DOI | MR | Zbl

[11] Le Bruyn L., Procesi C., “Semisimple representations of quivers”, Trans. Amer. Math. Soc., 317 (1990), 585–598 | DOI | MR | Zbl

[12] Molina Rojas L. A., Vistoli A., “On the Chow rings of classifying spaces for classical groups”, Rend. Sem. Mat. Univ. Padova, 116 (2006), 271–298, arXiv: math.AG/0505560 | MR | Zbl

[13] Mumford D., Fogarty J., Kirwan F., Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2), 34, 3rd ed., Springer-Verlag, Berlin, 1994 | DOI | MR

[14] Pabiniak M., Sabatini S., “Canonical bases for the equivariant cohomology and K-theory rings of symplectic toric manifolds”, J. Symplectic Geom., 16 (2018), 1117–1165, arXiv: 1503.04730 | DOI | MR | Zbl

[15] Reineke M., “Moduli of representations of quivers”, Trends in representation theory of algebras and related topics, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2008, 589–637, arXiv: 0802.2147 | DOI | MR | Zbl

[16] Reineke M., Stoppa J., Weist T., “MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence”, Geom. Topol., 16 (2012), 2097–2134, arXiv: 1110.4847 | DOI | MR | Zbl

[17] Reineke M., Weist T., “Refined GW/Kronecker correspondence”, Math. Ann., 355 (2013), 17–56, arXiv: 1103.5283 | DOI | MR | Zbl

[18] Rupel D., Weist T., “Cell decompositions for rank two quiver Grassmannians”, Math. Z., 295 (2020), 993–1038, arXiv: 1803.06590 | DOI | MR | Zbl

[19] Weist T., “Localization in quiver moduli spaces”, Represent. Theory, 17 (2013), 382–425, arXiv: 0903.5442 | DOI | MR | Zbl