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2004 | 2 | 3 | 478-492
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Weights in the cohomology of toric varieties

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
3
Strony
478-492
Opis fizyczny
Daty
wydano
2004-06-01
online
2004-06-01
Twórcy
Bibliografia
  • [1] C. Allday, V. Puppe: “On a conjecture of Goresky, Kottwitz and MacPherson”,Canad. J. Math., Vol. 51, (1999), pp. 3–9.
  • [2] G. Barthel, J.P. Brasselet, K.H. Fieseler, L. Kaup: “Equivariant intersection cohomology of toric varieties”,Contemp. Math., Vol. 241, (1999), pp. 45–68.
  • [3] G. Barthel, J.P. Brasselet, K.H. Fieseler, L. Kaup: “Combinatorial intersection cohomology for fans”,Tohoku Math. J., Vol. 2, (2002), pp. 1–41. http://dx.doi.org/10.2748/tmj/1113247177
  • [4] A.A. Beilinson, J. Bernstein, P. Deligne: “Pierre Faisceaux pervers”,Faisceaux pervers, Analysis and topology on singular spaces, I, (1981), pp. 5–171. (in French)
  • [5] M. Brion, R. Joshua: “Vanishing of old-dimensional intersection cohomology. II.”,Math. Ann., Vol. 321, (2001), pp. 399–437. http://dx.doi.org/10.1007/s002080100235
  • [6] J.L. Brylinski: “Equivariant intersection cohomology”,AMS Contemp. Math., Vol. 139, (1992), pp. 5–32.
  • [7] J.L. Brylinski, B. Zhang: “Equivariant Todd classes for toric varieties”,Preprint math. AG/0311318.
  • [8] V. M. Buchstaber, T. E. Panov: “Torus actions, combinatorial topology, and homological algebra”,Russ. Math. Surv., Vol. 55, (2000), pp. 825–921. (translated fromUsp. Mat. Nauk., Vol. 55, (2000), pp. 3–106) http://dx.doi.org/10.1070/rm2000v055n05ABEH000320
  • [9] J. Cheeger: “On the Hodge theory of Riemannian pseudomanifolds”,Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawai, 1979), Proc. Symp. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., (1980), pp. 91–146.
  • [10] J. Cheeger, M. Goresky, R. MacPherson: “L 2-cohomology and intersection homology of singular algebraic varieties”,Seminar on Differential Geometry, Ann. of Math. Stud., Princeton Univ. Press, Princeton, N.J., Vol. 102, (1982), pp. 303–340
  • [11] V. I. Danilov: “The geometry of toric varieties”,Russian Math. Surveys, Vol. 33, (1978), pp. 97–154. http://dx.doi.org/10.1070/RM1978v033n02ABEH002305
  • [12] P. Deligne: “La conjecture de Weil. I”,Inst. Hautes Études Sci. Publ. Math., Vol. 43, (1974), pp. 273–307; P. Deligne: “La conjecture de Weil. II”,Inst. Hautes Études Sci. Publ. Math., Vol. 52, (1980), pp. 137–252.
  • [13] P. Deligne: “Theorie de Hodge. II”,Publ. Math., Inst. Hautes Etud. Sci., Vol. 40, (1971), pp. 5–58.
  • [14] P. Deligne: “Theorie de Hodge. III”,Publ. Math., Inst. Hautes Etud. Sci., Vol. 44, (1974), pp. 5–77.
  • [15] J. Denef, F. Loeser: “Weights of exponential sums, intersection cohomology, and Newton polyhedra”,Inv. Math., Vol. 109, (1991), pp. 275–294. http://dx.doi.org/10.1007/BF01243914
  • [16] S. Eilenberg, J. C. Moore: “Homology and fibrations I. Coalgebras, cotensor product and its derived functors”,Comment. Math. Helv., Vol. 40, (1966), pp. 199–236.
  • [17] K.H. Fieseler: “Rational intersection cohomology of projective toric varieties”,J. Reine Angew. Math., Vol. 413, (1991), pp. 88–98.
  • [18] M. Franz: “Thesis: Koszul duality for tori”,Konstanz University, 2001.
  • [19] M. Franz:On the integral cohomology of smooth, toric varieties, Preprint math.AT/0308253.
  • [20] M. Franz, A. Weber: “Weights in cohomology and the Eilenberg-Moore spectral sequence”, preprinthttp://math.AG/0405589.
  • [21] W. Fulton: “Introduction to toric varieties. Annals of Mathematics Studies”,Princeton University Press Vol. 131, (1993), pp. 157.
  • [22] M. Goresky, R. Kottwitz, R. MacPherson: “Equivariant cohomology, Koszul duality and the localization theorem”,Inv. Math., Vol. 131, (1998), pp. 25–83. http://dx.doi.org/10.1007/s002220050197
  • [23] M. Goresky, R. MacPherson: “Intersection homology. II”,Invent. Math., Vol. 72, (1983), pp. 77–129. http://dx.doi.org/10.1007/BF01389130
  • [24] M.N. Ishida:Torus embeddings and algebraic intersection complexes I, II, algeom/9403008-9.
  • [25] J. Jurkiewicz: “Chow ring of projective nonsingular torus embedding”,Colloq. Math., Vol. 43, (1980), pp. 261–270.
  • [26] S. Lillywhite, “Formality in an equivariant setting”,Trans. Amer. Math. Soc., Vol. 355, pp. 2771–2793.
  • [27] T. Maszczyk, A. Weber: “Koszul duality for modules over Lie algebra”,Duke Math. J., Vol. 112, (2002), pp. 511–520. http://dx.doi.org/10.1215/S0012-9074-02-11234-4
  • [28] D. Notbohm, N. Ray: “On Davis Januszkiewicz Homotopy Types I; Formality and Rationalisation”, Preprint math.AT/0311167.
  • [29] T. Oda: “The algebraic de Rham theorem for toric varieties”,Tohoku Math. J., Vol. 2, (1993), pp. 231–247.
  • [30] C. Simpson:The topological realiztion of a simplicial presheaf, Preprint q-alg/9609004.
  • [31] L. Smith: “On the construction of the Eilenberg-Moore spectral sequence”,Bull. Amer. Math. Soc., Vol. 75, (1969), pp. 873–878. http://dx.doi.org/10.1090/S0002-9904-1969-12335-9
  • [32] B. Totaro: “Chow groups, Chow cohomology, and linear varieties”,Journal of Algebraic Geometry, to appear.http://www.dpmms.cam.ac.uk/∼bt219/papers.html
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475240
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