Journal of Algebraic Geometry

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		Online ISSN 1534-7486; Print ISSN 1056-3911

Sur la cohomologie de la puissance symétrique du fibré tautologique sur le schéma de Hilbert ponctuel d'une surface

Author(s): Gentiana Danila
Journal: J. Algebraic Geom. 13 (2004), 81-113.
Posted: August 5, 2003
MathSciNet review: 2008716
Retrieve article in: PDF

Abstract | References | Additional information

Abstract: We compute some cohomology spaces for the symmetric power of the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme $X^{\mbox{}^{[n]}}$ of a smooth projective surface on ${\mathbb C}$ .

References:

[Bout]: J. F. BOUTOT. Singularités rationnelles et quotients par les groupes réductifs. Invent. Math. 88 (1987) 65-68.
[Cheah]: J. CHEAH. The cohomology of smooth nested Hilbert schemes of points, Ph.D. thesis, University of Chicago, 1984.
[D1]: G. DANILA. Sections du fibré déterminant sur l'espace de modules des faisceaux semi-stables de rang sur le plan projectif. Ann. Inst. Fourier, Grenoble 50 (2000), no. 5, 1323-1374.
[D2]: G. DANILA. Sur la cohomologie d'un fibré tautologique sur le schéma de Hilbert d'une surface. Journal of Algebraic Geometry 10 (2001), no. 2, 247-280.
[Foga]: J. FOGARTY. Algebraic families on an algebraic surface. Amer. J. Math. 90 (1968), 511-521.
[Hart]: R. HARTSHORNE. Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, 1977.
[Lehn]: M. LEHN. Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent. Math. 136 (1999), no. 1, 157-207.
[Tikh]: A. TIKHOMIROV. On Hilbert schemes and flag varieties of points on algebraic surfaces, Preprint.

Additional Information:

Gentiana Danila
Affiliation: UMR 7586 du CNRS, Institut de Mathematiques, 2 Place Jussieu, 75251 Paris Cedex 05, France
Address at time of publication: Mathematical Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: gentiana@math.jussieu.fr, gentiana@maths.warwick.ac.uk
DOI: 10.1090/S1056-3911-03-00372-2
PII: S 1056-3911(03)00372-2
Received by editor(s): May 31, 2001
Posted: August 5, 2003

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