t, q-Catalan numbers and the Hilbert scheme

Discrete Mathematics

Volumn 193, Issue 1-3, 1998, Pages 201-224

  Haiman, Mark ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Catalan numbers; Hilbert scheme; Lefschetz formula; Sheaf cohomology

Indexed keywords

EID: 0000468027     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00141-1     Document Type: Article

References (20)

1. M.F. Atiyah, R. Bott, A Lefschetz fixed point formula for elliptic differential operators, Bull. A.M.S. 72 (1966) 245-250.
2. D. Bayer, M. Stillman, MACAULAY: A computer algebra system for algebraic geometry, version 3.0, Public domain computer program distributed by Harvard University, 1989.
3. P. Baum, W. Fulton, G. Quart, Lefschetz-Riemann-Roch for singular varieties, Acta Math. 143 (1979) 193-211.
4. n C{x, y}, Invent. Math. 41 (1977) 45-89.
5. L. Carlitz, J. Riordan, Two element lattice permutation numbers and their q-generalization, Duke J. Math. 31 (1964) 371-388.
6. G. Ellingsrud, S.A. Strömme, On the homology of the Hilbert scheme of points in the plane, Invent. Math. 87 (1987) 343-352.
7. J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968) 511-521.
8. J. Fogarty, Algebraic families on an algebraic surface, II. The Picard scheme of the punctual Hilbert scheme, Amer. J. Math. 95 (1973) 660-687.
9. A.M. Garsia, M. Haiman, A remarkable q, t-Catalan sequence and q-Lagrange inversion, J. Algebra Combin. (to appear).
10. M. Gordan, Les invariants des formes binaires, J. Math. Pures et Appl. (Liouville's J.) 6 (1900) 141-156.
11. G. Gotzmann, Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes, Math. Z. 158 (1978) 61-70.
12. A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique, IV: Les schemas de Hilbert, Séminaire Bourbaki 221, IHP, Paris, 1961.
13. M. Haiman, Conjectures on the quotient ring by diagonal invariants, J. Algebra Combin. 3 (1994) 17-76.
14. R. Hartshorne, Local cohomology, Lecture Notes in Mathematics 41, Springer, Berlin, 1967.
15. A. Iarrobino, Reducibility of the family of 0-dimensional subschemes on a variety, Invent. Math. 15 (1972) 72-77.
16. A. Iarrobino, Hilbert scheme of points: overview of last ten years, Algebraic Geometry, Bowdoin 1985, in: S.J. Bloch, (Ed.), Proceedings of Symposia in Pure Mathematics 46 part 2, A.M.S., Providence RI, 1987, 297-320.
17. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Clarendon Press, Oxford, England, 1995.
18. V.B. Mehta, A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. Math. 122 (1985) 27-40.
19. R.P. Stanley, Combinatorics and Commutative Algebra, Progr. Math. 41, Birkhäuser, Boston, Mass, 1983.
20. H. Weyl, The Classical Groups, Their Invariants and Representations, 2nd Ed., Princeton Univ. Press, Princeton, N.J, 1946.