This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.
[4] Cushman R.H., Bates L.M., Global Aspects of Classical Integrable Systems, Birkhäuser, Basel-Boston-Berlin, 1997 http://dx.doi.org/10.1007/978-3-0348-8891-2
[5] Duistermaat J.J., On global action-angle coordinates, Comm. Pure Appl. Math., 1980, 33(6), 687–706 http://dx.doi.org/10.1002/cpa.3160330602
[6] Flaschka H., A remark on integrable Hamiltonian systems, Phy. Lett. A, 1988, 131(9), 505–508 http://dx.doi.org/10.1016/0375-9601(88)90678-0
[7] Hurwitz A., Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen, 5th ed., Berlin-Heidelberg-New York, Springer, 2000 http://dx.doi.org/10.1007/978-3-642-56952-4
[8] Kas A., Weierstrass normal forms and invariants of elliptic surfaces, Trans. Amer. Math. Soc., 1977, 225, 259–266 http://dx.doi.org/10.1090/S0002-9947-1977-0422285-X
[9] Kodaira K., On compact analytic surfaces: I, II, III, Ann. of Math., 1960, 71, 111–152; 1963, 77, 563-626; 1963, 78, 1–40 http://dx.doi.org/10.2307/1969881
[10] Leung N.C., Symington M., Almost toric symplectic four-manifolds, J. Symplectic Geom., 2010, 8(2), 143–187