PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2003 | 1 | 4 | 418-434
Tytuł artykułu

Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
4
Strony
418-434
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Bibliografia
  • [1] [AB82] M.F. Atiyah and R. Bott: “The Yang-Mills equations over Riemann surfaces”, Philos. Trans. Roy. Soc. London Ser. A, Vol. 308, (1982), pp. 523–615.
  • [2] [AVGL91] V.I. Arnold, V.A. Vassiliev, V.V. Goryunov, O.V. Lyashko: “Singularities. Local and global theory”, Enc. Math. Sci. Dynamical Systems VI, Springer-Verlag, Berlin, 1991.
  • [3] [BF99] A. Buch and W. Fulton: “Chern class formulas for quiver varieties”, Inv. Math., Vol. 135, (1999), pp. 665–687. http://dx.doi.org/10.1007/s002220050297[Crossref]
  • [4] [CLL02] W. Chen, B. Li, J.D. Louck: “The flagged double schur function”, J. Algebraic Combin., Vol. 15, (2002), pp. 7–26. http://dx.doi.org/10.1023/A:1013217015135[Crossref]
  • [5] [FP89] W. Fulton and P. Pragacz: Schubert Varieties and Degeneracy Loci, Springer-Verlag, Berlin, 1998.
  • [6] [FR02] L. Fehér and R. Rimányi: “Classes of degeneraci loci for quivers-the Thom polynomial point of view”, Duke J. Math., Vol. 114, (2002), pp. 193–213. http://dx.doi.org/10.1215/S0012-7094-02-11421-5[Crossref]
  • [7] [FR03] L. M. Fehér and R. Rimányi: “Calculation of Thom polynomials and other cohomological obstructions for group actions”, to appear in Sao Carlos Singularities 2002, Cont. Math. AMS, 2003.
  • [8] [FRN03] L. Fehér, A. Némethi, R. Rimányi: Coincident root loci of binary forms, http://www.math.ohio-state.edu/∼rimanyi/cikkek, 2003.
  • [9] [Ful92] W. Fulton: “Flags, Schubert polynomials, degeneracy loci, and determinantal formulas”, Duke Math. J., Vol. 65, (1992), pp. 381–420. http://dx.doi.org/10.1215/S0012-7094-92-06516-1[Crossref]
  • [10] [Ful98] W. Fulton: Intersection Theory. Springer, Berlin, 1984, 1998. [WoS]
  • [11] [Kaz95] M. Kazarian: “Characteristic classes of Lagrange and Legendre singularities”, Russian Math. Surv., Vol. 50, (1995), pp. 701–726. http://dx.doi.org/10.1070/RM1995v050n04ABEH002579[Crossref]
  • [12] [Kaz97] M.É. Kazarian: “Characteristic classes of singularity theory”, In: V.I. Arnold et al., (Eds): The Arnold-Gelfand mathematical seminars: geometry and singularity theory, Birkhauser Boston, Boston MA, 1997, pp. 325–340.
  • [13] [Kaz00] M. Kazarian: “Thom polynomials for Lagrange, Legendre and critical point singularities”, Isaac Newton Institute for Math. Sci., preprint, 2000.
  • [14] [Kir84] F. Kirwan: Cohomology of quotients in symplectic and algebraic geometry. No. 31, in Mathematical Notes, Princeton University Press, Princeton NY, 1984.
  • [15] [Kir92] F. Kirwan: “The cohomology rings of moduli spaces of bundles over Riemann surfaces”, J. Amer. Math. Soc., Vol. 5, (1992), pp. 853–906. http://dx.doi.org/10.2307/2152712[Crossref]
  • [16] [KL74] G. Kempf and D. Laksov: “The determinantal formula of Schubert calculus”, Acta. Math., Vol. 132, (1974), pp. 153–162. http://dx.doi.org/10.1007/BF02392111[Crossref]
  • [17] [Las74] Alain Lascoux: “Puissances extérieures, déterminants et cycles de Schubert”, Bull. Soc. Math. France, Vol. 102, (1974), pp. 161–179.
  • [18] [LS82] Lascoux and Schützenberger: “Polynômes de Schubert”, C. R. Acad. Sci. Paris, Vol. 294, (1982), pp. 447–450.
  • [19] [Mac91] I.G. MacDonald: Notes on Schubert polynomials, LACIM 6, 1991.
  • [20] [Pra88] Piotr Pragacz: “Enumerative geometry of degeneracy loci”, Ann. Sci. École Norm. Sup. (4), Vol. 21, (1988), pp. 413–454.
  • [21] [Rim01] R. Rimányi: “Thom polynomials, symmetries and incidences of singularities”, Inv. Math., Vol. 143, (2001), pp. 499–521. http://dx.doi.org/10.1007/s002220000113[Crossref]
  • [22] [Sti36] E. Stiefel: “Richtungsfelder und Fernparallelismus in Mannigfaltigkeiten”, Comm. Math. Helv., Vol. 8, (1936), pp. 3–51.
  • [23] [Szű79] A. Szűcs: “Analogue of the Thom space for mapping with singularity of type ∑1”, Math. Sb. (N. S.), Vol. 108, (1979), pp. 438–456.
  • [24] [Vas88] V.A. Vassiliev: Lagrange and Legendre Characteristic Classes, Gordon and Breach, New York, 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475176
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.