Contraction of excess fibres between the McKay correspondences in dimensions two and three
Samuel Boissière[1]; Alessandra Sarti[2]
- [1] Université de Nice Sophia-Antipolis Laboratoire J.A.Dieudonné UMR CNRS 6621 Parc Valrose 06108 Nice (France)
- [2] Johannes Gutenberg Universität Mainz Institut für Mathematik 55099 Mainz (Deutschland)
Annales de l’institut Fourier (2007)
- Volume: 57, Issue: 6, page 1839-1861
- ISSN: 0373-0956
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top- M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra, (1969), Addison-Wesley Zbl0175.03601MR242802
- W. P. Barth, A. Sarti, Polyhedral Groups and Pencils of K3-Surfaces with Maximal Picard Number, Asian J. of Math. 7 (2003), 519-538 Zbl1063.14047MR2074889
- T. Bridgeland, A. King, M. Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14 (2001), 535-554 Zbl0966.14028MR1824990
- W. Crawley-Boevey, On the exceptional fibres of Kleinian singularities, Amer. J. Math. 122 (2000), 1027-1037 Zbl1001.14001MR1781930
- J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511-521 Zbl0176.18401MR237496
- Y. Gomi, I. Nakamura, K.-I. Shinoda, Hilbert schemes of -orbits in dimension three, Asian J. Math. 4 (2000), 51-70 Zbl0981.14002MR1802912
- Y. Gomi, I. Nakamura, K.-I. Shinoda, Coinvariant algebras of finite subgroups of , Can. J. Math. 56 (2002), 495-528 Zbl1066.14053MR2057284
- G. Gonzalez-Sprinberg, J.-L. Verdier, Construction géométrique de la correspondance de McKay, Ann. scient. Éc. Norm. Sup. 16 (1983), 409-449 Zbl0538.14033MR740077
- R. Hartshorne, Algebraic geometry, (1977), Springer Zbl0367.14001MR463157
- D. Huybrechts, M. Lehn, The geometry of moduli spaces of sheaves, (1997), Vieweg Zbl0872.14002MR1450870
- Y. Ito, H. Nakajima, McKay correspondence and Hilbert schemes in dimension , Topology 39 (2000), 1155-1191 Zbl0995.14001MR1783852
- Y. Ito, I. Nakamura, McKay correspondence and Hilbert schemes, Proc. Japan. Acad. 92 (1996), 135-138 Zbl0881.14002MR1420598
- Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (1999), 151-233, Camb. Univ. Press Zbl0954.14001MR1714824
- M. Kapranov, E. Vasserot, Kleinian singularities, derived categories and Hall algebras, Math. Ann. 316 (2000), 565-576 Zbl0997.14001MR1752785
- J. McKay, Graphs, singularities and finite groups, Proc. of Symp. in Pure Math. 37 (1980), 183-186 Zbl0451.05026MR604577
- I. Nakamura, Hilbert scheme of abelian group orbits, J. Alg. Geom. 10 (2001), 757-779 Zbl1104.14003MR1838978
- A. Sarti, Pencils of Symmetric Surfaces in , J. of Algebra 246 (2001), 429-452 Zbl1064.14038MR1872630
- S. Térouanne, Correspondance de McKay : variations en dimension trois, (2004)