Weights in the cohomology of toric varieties
Open Mathematics (2004)
- Volume: 2, Issue: 3, page 478-492
- ISSN: 2391-5455
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] C. Allday, V. Puppe: “On a conjecture of Goresky, Kottwitz and MacPherson”,Canad. J. Math., Vol. 51, (1999), pp. 3–9. Zbl0954.18005
- [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. Zbl0970.14028
- [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 Zbl1055.14024
- [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 Zbl0997.14005
- [6] J.L. Brylinski: “Equivariant intersection cohomology”,AMS Contemp. Math., Vol. 139, (1992), pp. 5–32. Zbl0803.55002
- [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 Zbl1010.52011
- [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 Zbl0503.14008
- [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 Zbl0425.14013
- [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 Zbl0763.14025
- [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. Zbl0148.43203
- [17] K.H. Fieseler: “Rational intersection cohomology of projective toric varieties”,J. Reine Angew. Math., Vol. 413, (1991), pp. 88–98. Zbl0716.14006
- [18] M. Franz: “Thesis: Koszul duality for tori”,Konstanz University, 2001. Zbl0978.55004
- [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. Zbl1145.14021
- [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 Zbl0897.22009
- [23] M. Goresky, R. MacPherson: “Intersection homology. II”,Invent. Math., Vol. 72, (1983), pp. 77–129. http://dx.doi.org/10.1007/BF01389130 Zbl0529.55007
- [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. Zbl0524.14005
- [26] S. Lillywhite, “Formality in an equivariant setting”,Trans. Amer. Math. Soc., Vol. 355, pp. 2771–2793. Zbl1021.55006
- [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 Zbl1014.17018
- [28] D. Notbohm, N. Ray: “On Davis Januszkiewicz Homotopy Types I; Formality and Rationalisation”, Preprint math.AT/0311167. Zbl1065.55006
- [29] T. Oda: “The algebraic de Rham theorem for toric varieties”,Tohoku Math. J., Vol. 2, (1993), pp. 231–247. Zbl0776.14003
- [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 Zbl0177.51403
- [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 Zbl1329.14018