You can download the excercise sheets for the school SinG 2024 here

• Exercise sheet on K3 surfaces: here

• Exercise sheet on IHS manifolds: here

The following is a list of references for the topics that will be covered at SinG 2024

• A. Garbagnati, A. Sarti, Symplectic automorphisms of prime order on K3 surfaces, J. of Algebra 318 (2007) 323–350

• A. Garbagnati, A. Sarti, Elliptic fibrations and symplectic automorphisms on K3 surfaces, Comm. in Algebra, 37 (2009), no. 10, 3601–3631.

• M. Artebani, S. Taki, A. Sarti, K3 surfaces with non-symplectic automorphisms of prime order (with an appendix by S. Kondo), Math. Z., (2011), 268, 507–533.

• S. Boissière, M. Nieper-Wisskirchen, A. Sarti, Smith Theory and Irreducible Holomorphic Symplectic Manifolds, J. of Topology 6 (2013), no. 2, 361–390.

• S. Boissière, C. Camere, A. Sarti, Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices, Kyoto J. Math. 56 (2016), no. 3, 465–499.

• S. Boissière, C. Camere, A. Sarti, Complex ball quotients from manifolds of K3[n] type, J. Pure Appl. Algebra 223 (2019), no. 3, 1123–1138.

• S. Boissière, C. Camere, A. Sarti, Cubic threefolds and hyperkähler manifolds uniformized by the 10-dimensional complex ball, Math. Ann. 373 (2019), no. 3-4, 1429– 1455.

• C. Bonnafé, A. Sarti, Complex Reflection Groups and K3 surfaces I, Épijournal G ́eom. Algébrique 5 (2021), Art. 3.

• C. Bonnafé, A. Sarti, Complex Reflection Groups and K3 surfaces II. The groups G29, G30 and G31. To appear in J. Korean Math. Soc.

• P. Comparin, N. Priddis, On some K3 surfaces with order 16 automorphism. To appear in Math. Nachrichten.

• R. Bell, P. Comparin, J. Li, A. Rincón-Hidalgo, A. Sarti, A. Zanardini, Non-symplectic automorphisms of order multiple of seven on K3 surfaces. Preprint

• V. V. Nikulin. Finite groups of automorphisms of Kählerian K3 surfaces. Trudy Moskov. Mat. Obshch., 38:75–137, 1979.

• V. V. Nikulin. Integer symmetric bilinear forms and some of their geometric applications. Izv. Akad. Nauk SSSR Ser. Mat., 43(1):111–177, 238, 1979.

• D. Huybrechts, Compact hyper-Kähler manifolds: basic results, Invent. Math. 135 (1999), no. 1, 63–113.

• E. Markman, A survey of Torelli and monodromy results for holomorphic-symplectic varieties, Complex and differential geometry, Springer Proc. Math., vol. 8, Springer, Heidelberg, 2011, pp. 257–322.

• A. Beauville, Some remarks on Kähler manifolds with c1 = 0, Classification of algebraic and analytic manifolds (Katata, 1982), Progr. Math., vol. 39, pp. 1–26.

• A. Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Diff. Geom. 18 (1983), no. 4, 755–782 (1984).