Symplectic Automorphisms and the Picard Group of a K3 Surface

REFERENCES

• Barth , W. P. , Hulek , K. , Peters , C. A. M. , Van de Ven , A. ( 2004 ). Compact Complex Surfaces . Berlin : Springer .
   Google Scholar
• Batyrev , V. , Cox , D. ( 1994 ). On the Hodge structure of projective hypersurfaces in toric varieties . Duke Mathematical Journal 75 ( 2 ): 293 – 338 .
   Web of Science ®Google Scholar
• Bertin , J. ( 1988 ). Réseaux de Kummer et surfaces K3 . Inventiones Mathematicae 93 ( 2 ): 267 – 284 .
   Web of Science ®Google Scholar
• Bosma , W. , Cannon , J. , Playoust , C. ( 1997 ). The Magma algebra system. I. The user language . Journal of Symbolic Computation 24 ( 3–4 ): 235 – 265 .
   Web of Science ®Google Scholar
• Campana , F. ( 2004 ). Orbifoldes à Première Classe de Chern Nulle. The Fano Conference, Univ. Torino, Turin, pp. 339–351 .
   Google Scholar
• Cartan , H. , Eilenberg , S. ( 1956 ). Homological Algebra . Princeton : Princeton University Press
   Google Scholar
• Cox , D. ( 1996 ). Toric residues . Arkiv för Matematik 34 ( 1 ): 73 – 96 .
   Web of Science ®Google Scholar
• Cox , D. , Katz , S. ( 1999 ). Mirror Symmetry and Algebraic Geometry . Providence : American Mathematical Society .
   Google Scholar
• Doran , C. , Kerr , M. ( 2008 ). Algebraic K-theory of toric hypersurfaces. arXiv, math.AG/0809.4669 .
   Google Scholar
• Fujiki , A. ( 1988 ). Finite automorphism groups of complex tori of dimension two . Publications of the Research Institute for Mathematical Sciences 24 ( 1 ): 1 – 97 .
   Web of Science ®Google Scholar
• Garbagnati , A. ( 2010 ). Symplectic Automorphisms on Kummer Surfaces . Geom. Dedicata 145 : 219 – 232 .
   Web of Science ®Google Scholar
• Garbagnati , A. ( 2008 ). The Dihedral Group 𝒟5 as Group of Symplectic Automorphisms on K3 Surfaces. arXiv, math.AG/0812.4518 .
   Google Scholar
• Garbagnati , A. ( 2009 ). Elliptic K3 surfaces with abelian and dihedral groups of symplectic automorphisms. arXiv, math.AG/0904.1519 .
   Google Scholar
• Garbagnati , A. , Sarti , A. ( 2007 ). Symplectic automorphisms of prime on K3 surfaces . Journal of Algebra 318 ( 1 ): 323 – 350 .
   Web of Science ®Google Scholar
• Hashimoto , K. ( 2009 ). Period map of a certain K3 family with an 𝒮5-action. arXiv, math.AG/0904.0072 .
   Google Scholar
• Hosono , S. , Lian , B. H. , Oguiso , K. , Yau , S.-T. ( 2004 ). Autoequivalences of derived category of a K3 surface and monodromy transformations . Journal of Algebraic Geometry 13 ( 3 ): 513 – 545 .
   Web of Science ®Google Scholar
• Keum , J. , Oguiso , K. , Zhang , D.-Q. ( 2005 ). The alternating group of degree 6 in the geometry of the Leech lattice and K3 surfaces . Proc. London Math. Soc. (3) 90 ( 2 ): 371 – 394 .
   Web of Science ®Google Scholar
• Keum , J. , Oguiso , K. , Zhang , D.-Q. ( 2007 ). Extensions of the alternating group of degree 6 in the geometry of K3 surfaces . European Journal of Combinatorics 28 ( 2 ): 549 – 558 .
   Web of Science ®Google Scholar
• Kondō , S. ( 1998 ). Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of K3 surfaces. With an appendix by Shigeru Mukai . Duke Mathematical Journal 92 ( 3 ): 593 – 603 .
   Web of Science ®Google Scholar
• Morrison , D. R. ( 1984 ). On K3 surfaces with large Picard number . Inventiones Mathematicae 75 ( 1 ): 105 – 121 .
   Web of Science ®Google Scholar
• Mukai , S. ( 1988 ). Finite groups of automorphisms and the Mathieu group . Inventiones Mathematicae 94 ( 1 ): 183 – 221 .
   Web of Science ®Google Scholar
• Narumiya , N. , Shiga , H. ( 2001 ). The mirror map for a family of K3 surfaces induced from the simplest 3-dimensional reflexive polytope . Proceedings on Moonshine and Related Topics . Providence , RI : American Mathematical Society , pp. 139 – 161 .
   Google Scholar
• Nikulin , V. ( 1980 ). Finite automorphism groups of Kähler K3 surfaces . Transactions of the Moscow Mathematical Society 38 ( 2 ): 71 – 135 .
   Google Scholar
• Nikulin , V. (1980). Integral symmetric bilinear forms and some of their geometric applications. Math USSR-Izv. 14(1):103–167.
   Web of Science ®Google Scholar
• Oguiso , K. ( 2003 ). A characterization of the Fermat quartic K3 surface by means of finite symmetries . Compos. Math. 141 ( 2 ): 404 – 424 .
   Web of Science ®Google Scholar
• Önsiper , H. , Sertöz, S. ( 1999 ). Generalized Shioda-Inose structures on K3 surfaces . Manuscripta Mathematica 98 ( 4 ): 491 – 495 .
   Web of Science ®Google Scholar
• Oguiso , K. , Zhang , D.-Q. ( 2002 ). The simple group of order 168 and K3 surfaces . Complex Geometry (Göttingen, 2000) . Berlin : Springer , pp. 165 – 184 .
   Google Scholar
• SAGE Mathematics Software, Version 3.4. Software available at http://www.sagemath.org/
   Google Scholar
• Shimada , I. , Zhang , D.-Q. ( 2001 ). Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces . Nagoya Mathematical Journal 161 : 23 – 54 .
   Web of Science ®Google Scholar
• Smith , J. P. ( 2006 ). Picard-Fuchs Differential Equations for Families of K3 Surfaces. Ph.D. diss., University of Warwick .
   Google Scholar
• Todorov , A. N. ( 1980 ). Applications of the Kahler–Einstein Calabi–Yau metric to moduli of K3 surfaces . Inventiones Mathematicae 61 ( 3 ): 251 – 265 .
   Web of Science ®Google Scholar
• Xiao , G. ( 1996 ). Galois covers between K3 surfaces . Annales de l'Institut Fourier 46 ( 1 ): 73 – 88 .
   Web of Science ®Google Scholar
• Communicated by C. Pedrini.
   Google Scholar