K3-surfaces

Want to see a K3?

Projective K3-surfaces with fixed polarization of degree d have a quasi-projective moduli space, say M_d. There is a recent rather complete result on the Kodaira dimension of the moduli spaces M_d:
V. Gritsenko, K. Hulek, G.K. Sankaran: The Kodaira dimension of the moduli of K3 surfaces ArXiv/math /0607339

Some recent and not so recent results on special K3-surfaces with specific automorphisms :

Michela Artebani: A one dimensional family of K3 surfaces with a Z₄ action ArXiv/math 0605152
Michela Artebani, Alessandra Sarti: Non-symplectic automorphisms of order 3 on K3 surfaces ArXiv/math 0801.3101
Igor Dolgachev, JongHae Keum: K3 surfaces with a symplectic automorphism of order 11, ArXiv/math /0602518
Federica Galluzzi, Giuseppe Lombardo, Chris Peters: Automorphs of indefinite binary quadratic forms and K3-surfaces with Picard number 2 ArXiv/math/0804.0725
Alice Garbagnati, Alessandra Sarti: Symplectic automorphisms of prime order on K3 surfaces, J. of Algebra 318 (2007) 323-350 ArXiv/math//0603742
Alice Garbagnati, Alessandra Sarti: Elliptic fibrations and symplectic automorphisms on K3 surfaces ArXiv/math/0801.3992
Bert van Geemen, Alessandra Sarti: Nikulin involutions on K3 surfaces, Math. Z. 255 (2007), no. 4, 731-753 ArXiv/math/0602015
Ximin Liu, Nobuhiro Nakamura: Pseudofree Z/3-actions on K3 surfaces ArXiv/math/0604317
Keiji Oguiso, De-Qi Zhang : The Simple Group of Order 168 and K3 Surfaces ArXiv/math/0011259
K. Oguiso, D. -Q. Zhang: K3 surfaces with order 11 automorphisms ArXiv/math/9907020
D. -Q. Zhang: The Alternating Groups and K3 Surfaces ArXiv/math/0506610

Relations with group theory:

Richard E. Borcherds: Coxeter groups, Lorentzian lattices, and K3 surfaces, arXiv/math/9806141
Sarti, A.: A geometrical construction for the polynomial invariants of some reflection groups, Serdica Math. J., 31, pp. 229-242, 2005
Sarti, A: Group Actions, cyclic coverings and families of K3-surfaces, Canad. Math. Bull. 49 (4), 2006 pp. 592-608

Correspondences

Federica Galluzzi, Giuseppe Lombardo: Correspondences between K3 surfaces arXiv/math/0211129
Carlo Madonna, Viacheslav V. Nikulin: On a classical correspondence between K3 surfaces arXiv/math/020615
Carlo Madonna, Viacheslav V. Nikulin: On a classical correspondence between K3 surfaces II arXiv/math/0304415
Carlo Madonna, Viacheslav V. Nikulin: On a classical correspondence between K3 surfaces III, arXiv/math/0605362
H. Onsiper, S. Sertoz: Generalized Shioda-Inose Structures on K3 Surfaces, arXiv/math/9809083