Abstract
The purpose of this paper is to investigate relationship between the automorphism group of a rational surface and that of its Hilbert scheme of n points.
Similar content being viewed by others
References
Arapura, D., Archava, S.: Kodaira dimension of symmetric powers. Proc. Am. Math. Soc. 131(5), 1369–1372 (2003). (electronic)
Arcara, D., Bertram, A., Coskun, I., Huizenga, J.: The minimal model program for the Hilbert scheme of points on \({\mathbb{P}}^{2}\) and Bridgeland stability. Adv. Math. 235, 580–626 (2013). (English summary)
Artebani, M., Laface, A.: Cox rings of surfaces and the anticanonical Iitaka dimension. Adv. Math. 226(6), 5252–5267 (2011)
Beauville, A.: Some remarks on Kähler manifolds with c\(_{1}\)=0. In: Ueno, K. (ed.) Classification of Algebraic and Analytic Manifolds (Katata, 1982), pp. 1–26. Progr. Math., vol. 39. Birkhäuser, Boston (1983)
Belmans, P., Oberdieck, G., Rennemo, J.: Automorphisms of Hilbert Schemes of Points on Surfaces. arXiv:1907.07064
Bertram, A., Coskun, I.: The birational geometry of the Hilbert schemes of points on surfaces. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds.) Birational Geometry, Rational Curves, and Arithmetic, pp. 15–55. Springer, New York (2013)
Boissière, S.: Automorphismes naturels de l’espace de Douady de points sur une surface. Can. J. Math. 64(1), 3–23 (2012)
Boissière, S., Sarti, A.: A note on automorphisms and birational transformations of holomorphic symplectic manifolds. Proc. Am. Math. Soc. 140(12), 4053–4062 (2012)
Boissière, S., Cattaneo, A., Nieper-Wisskirchen, M., Sarti, A.: Higher dimensional enriques varieties and automorphisms of generalized Kummer varieties. J. Math. Pures Appl. (9) 95(5), 553–563 (2011)
Boissière, S., Cattaneo, A., Nieper-Wisskirchen, M., Sarti, A.: The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface. In: Proceedings of the Schiermonnikoog conference, K3 surfaces and their moduli, Progress in Mathematics 315. Birkhäuser (2015)
Bolognese, B., Huizenga, J., Lin, Y., Riedl, E., Schmidt, B., Woolf, M., Zhao, X.: Nef cones of Hilbert schemes of points on surfaces. Algebra Number Theory 10(4), 907–930 (2016)
Brion, M., Kumar, S.: Frobenius splitting methods in geometry and representation theory. Progress in Mathematics, vol. 231. Birkhäuser, Boston (2005)
Cattaneo, A.: Automorphisms of Hilbert Schemes of Points on a Generic Projective K3 Surface. arXiv:1801.05682
Fogarty, J.: Algebraic families on an algebraic surface. Am. J. Math. 90, 511–521 (1968)
Fogarty, J.: Algebraic families on an algebraic surface II: The Picard scheme of the punctual Hilbert scheme. Am. J. Math. 95, 660–687 (1973)
Göttsche, L., Soergel, W.: Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces. Math. Ann. 296, 235–245 (1993)
Hassett, B., Tschinkel, Y.: Extremal Rays and Automorphisms of Holomorphic Symplectic Varieties. arXiv:1506.08153
Hayashi, T.: Universal covering calabi-yau manifolds of the hilbert schemes of n points of enriques surfaces. Asian J. Math 21(6), 1099–1120 (2017)
Huybrechts, D., Lehnl, M.: The Geometry of Moduli Spaces of Sheaves. Aspects of Mathematics E31. Friedr. Vieweg and Sohn, Braunschweig (1997)
Li, W.-P., Qin, Z., Zhang, Q.: Curves in the Hilbert schemes of points on surfaces. Contemp. Math. 322, 89–96 (2003)
Oguiso, K.: On automorphisms of the punctual Hilbert schemes of K3 surfaces. Eur. J. Math. 2(1), 246–261 (2016)
Sosna, P.: Fourier-Mukai partners of canonical covers of bielliptic and enriques surfaces. Rend. Sem. Mat. Univ. Padova 130, 203–213 (2013)
Testa, D., Várilly-Alvarado, A., Velasco, M.: Big rational surfaces. Math. Ann. 351(1), 95–107 (2011)
Yoshioka, K.: Moduli spaces of stable sheaves on abelian surfaces. Math. Ann. 321(4), 817–884 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hayashi, T. Automorphisms of the Hilbert schemes of n points of a rational surface and the anticanonical Iitaka dimension. Geom Dedicata 207, 395–407 (2020). https://doi.org/10.1007/s10711-019-00504-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-019-00504-7