Sur la cohomologie de la puissance symétrique du fibré tautologique sur le schéma de Hilbert ponctuel d’une surface
Author:
Gentiana Danila
Journal:
J. Algebraic Geom. 13 (2004), 81-113
DOI:
https://doi.org/10.1090/S1056-3911-03-00372-2
Published electronically:
August 5, 2003
MathSciNet review:
2008716
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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 $X$ on ${\mathbb C}$.
[Bout]Bou J. F. Boutot. Singularités rationnelles et quotients par les groupes réductifs. Invent. Math. 88 (1987) 65-68.
[Cheah]Che J. Cheah. The cohomology of smooth nested Hilbert schemes of points, Ph.D. thesis, University of Chicago, 1984.
[D1]Danila1 G. Danila. Sections du fibré déterminant sur l’espace de modules des faisceaux semi-stables de rang $2$ sur le plan projectif. Ann. Inst. Fourier, Grenoble 50 (2000), no. 5, 1323-1374.
[D2]Danila 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]Fogarty J. Fogarty. Algebraic families on an algebraic surface. Amer. J. Math. 90 (1968), 511-521.
[Hart]Hart R. Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, 1977.
[Lehn]Lehn M. Lehn. Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent. Math. 136 (1999), no. 1, 157–207.
[Tikh]Tik A. Tikhomirov. On Hilbert schemes and flag varieties of points on algebraic surfaces, Preprint.
[Bout]Bou J. F. Boutot. Singularités rationnelles et quotients par les groupes réductifs. Invent. Math. 88 (1987) 65-68.
[Cheah]Che J. Cheah. The cohomology of smooth nested Hilbert schemes of points, Ph.D. thesis, University of Chicago, 1984.
[D1]Danila1 G. Danila. Sections du fibré déterminant sur l’espace de modules des faisceaux semi-stables de rang $2$ sur le plan projectif. Ann. Inst. Fourier, Grenoble 50 (2000), no. 5, 1323-1374.
[D2]Danila 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]Fogarty J. Fogarty. Algebraic families on an algebraic surface. Amer. J. Math. 90 (1968), 511-521.
[Hart]Hart R. Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, 1977.
[Lehn]Lehn M. Lehn. Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent. Math. 136 (1999), no. 1, 157–207.
[Tikh]Tik 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
Received by editor(s):
May 31, 2001
Published electronically:
August 5, 2003
