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Automorphismes naturels de l'espace de Douady de points sur une surface

Published online by Cambridge University Press:  20 November 2018

Samuel Boissière*
Affiliation:
Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France URL: http://www-math.sp2mi.univ-poitiers.fr/~sboissie/ email: [email protected]
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Résumé

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On établit quelques résultats généraux relatifs à la taille du groupe d’automorphismes de l’espace de Douady de points sur une surface, puis on étudie quelques propriétés des automorphismes provenant d’un automorphisme de la surface, en particulier leur action sur la cohomologie et la classification de leurs points fixes.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

References

Références

[1] Beauville, A., Some remarks on Kähler manifolds with c1 = 0. In: Classification of algebraic and analytic manifolds (Katata, 1982), Progr. Math. 39(1983), 1-26.Google Scholar
[2] Beauville, A., Variétés Kähleriennes dont la première classe de Chern est nulle. J. Differential Geom. 18(1983), 755-782.Google Scholar
[3] Bochner, S. and Montgomery, D. M., Groups on analytic manifolds. Ann. Math. 48(1947), 659-669. http://dx. doi. org/10.2307/1969133Google Scholar
[4] Boissière, S. and Sarti, A., A note on automorphisms and birational transformations of holomorphic symplectic manifolds. Proc. Amer. Math. Soc., à parâıtre.Google Scholar
[5] Briançon, J., Description de Hilbn C﹛x, y. Invent. Math. 41(1977), 45-89. http://dx. doi. org/10.1007/BF01390164Google Scholar
[6] Cheah, J., On the cohomology of Hilbert schemes of points. J. Algebraic Geom. 5(1996), 479-511.Google Scholar
[7] de Cataldo, M. A. and Migliorini, L., The Douady space of a complex surface. Adv. Math. 151(2000), 283-312. http://dx. doi. org/10.1006/aima.1999.1896Google Scholar
[8] Douady, A., Le problème des modules pour les sous-espaces analytiques compacts d’un espace analytique donné. Ann. Inst. Fourier (Grenoble) 16(1966), 1-95.Google Scholar
[9] Eisenbud, D. and Harris, J., The geometry of schemes. Graduate Texts in Mathematics 197, Springer-Verlag, New York, 2000.Google Scholar
[10] Fogarty, J., Algebraic families on an algebraic surface. Amer. J. Math. 90(1968), 511-521. http://dx. doi. org/10.2307/2373541Google Scholar
[11] Fogarty, J., Algebraic families on an algebraic surface. II. The Picard scheme of the punctual Hilbert scheme. Amer. J. Math. 95(1973), 660-687. http://dx. doi. org/10.2307/2373734Google Scholar
[12] Fujiki, A., Countability of the Douady space of a complex space. Japan. J. Math. (N. S.) 5(1979), 431-447.Google Scholar
[13] Garbagnati, A. and Sarti, A., Symplectic automorphisms of prime order on K3 surfaces. J. Algebra 318(2007), 323-350. http://dx. doi. org/10.1016/j. jalgebra.2007.04.017Google Scholar
[14] Godement, R., Introduction à la théorie des groupes de Lie. Publications Mathématiques de l’Université Paris VII, Université de Paris VII, U. E. R. de Mathématiques, Paris, 1982.Google Scholar
[15] Göttsche, L., The Betti numbers of the Hilbert scheme of points on a smooth projective surface. Math. Ann. 286(1990), 193-207. http://dx. doi. org/10.1007/BF01453572Google Scholar
[16] Grothendieck, A., Techniques de construction et théorèmes d’existence en géométrie algébrique. IV. Les schémas de Hilbert. In: Séminaire Bourbaki vol. 6, Exp. No. 221, Soc. Math. France, Paris, 1995, 249-276.Google Scholar
[17] Huybrechts, D., Compact hyper-Kähler manifolds: basic results. Invent. Math. 135(1999), 63-113. http://dx. doi. org/10.1007/s002220050280Google Scholar
[18] Kerner, H., Über die Automorphismengruppen kompakter komplexer Räume. Arch. Math. 11(1960), 282-288.Google Scholar
[19] Lehn, M., Lectures on Hilbert schemes. In: Algebraic structures and moduli spaces CRM Proc. Lecture Notes 38, Amer. Math. Soc., Providence, RI, 2004, 1-30.Google Scholar
[20] Lehn, M. and Sorger, C., The cup product of Hilbert schemes for K3 surfaces. Invent. Math. 152(2003), 305-329. http://dx. doi. org/10.1007/s00222-002-0270-7Google Scholar
[21] McMullen, C. T., Dynamics on K3 surfaces: Salem numbers and Siegel disks. J. Reine Angew. Math. 545(2002), 201-233. http://dx. doi. org/10.1515/crll.2002.036Google Scholar
[22] Nakajima, H., Heisenberg algebra and Hilbert schemes of points on projective surfaces. Ann. of Math. 145(1997), 379-388. http://dx. doi. org/10.2307/2951818Google Scholar
[23] Nieper-Wißkirchen, M., Chern numbers and Rozansky-Witten invariants of compact hyper-Kähler manifolds. World Scientific Publishing Co., Inc., River Edge, NJ, 2004.Google Scholar
[24] Nikulin, V. V., Finite groups of automorphisms of Kählerian K3 surfaces. Trudy Moskov. Mat. Obshch. 38(1979), 75-137.Google Scholar
[25] Steenbrink, J. H. M., Mixed Hodge structure on the vanishing cohomology. In: Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, 525-563.Google Scholar