A Note on Automorphisms and Birational Transformations of Holomorphic Symplectic Manifolds

For finitely generated group that are linear over a field, a polynomial upper bound for these functions is established in [BM], and in the case of higher rank arithmetic groups,

is the disjoint union of a twisted cubic and a line, so this case gives an irreducible family, and the general element belongs to E 12.. Let us follow the strategy

For instance, the set of all dynamical degrees of birational transformations of the complex projective plane is a closed and well ordered set of algebraic numbers.. An important

In general c^aux will not be closed, and in view of the minimal coupling hor- izontal component of i9 we see that o;aux 7^ ^(i) when P is not flat. On the other hand, we have S^ = uj^

(The global analyticity of the type change locus will be addressed in upcoming work.) So as a consequence of the Main Theorem, the local structure is not too badly

Our objective is to extend this fact to a result that birational, finitely generated, flat extensions of integral domains are open-immersions.. In addi- tion, we show that

For Theorem 2, the idea will be to stabilize the boundary so that the pages of a given planar open book can be lifted to holomorphic curves in the cylindrical end—we can then

In fact, all real analytic non-degenerate functions are locally equivalent under holomorphic symplectic transformation.. This is a consequence of the real